Fire crews battled for hours to contain the blaze which broke out at Herdman's Mill in Sion Mills in the early hours.
Fire crews were first alerted at about 0120 BST but the blaze later re-ignited and burned for several hours.
Mr Attwood said he would work to save the mill which featured in the BBC television series Restoration in 2003.
Last week, Ulster Bank appointed a receiver to the building.
The move ended more than 170 years of ownership for the Herdman family.
The former owners of the historic mill said they feared it may have been completely destroyed by the fire.
Forty fire officers were needed to deal with the blaze which was brought under control in the late afternoon.
Fire-fighters, who used two high-reach appliances while battling the blaze, are expected to remain at the scene until late on Saturday.
Mr Attwood said: "Our built heritage is a vital cog in our tourism industry and this fire greatly concerns me.
"The fire at the Mill damages a jewel in our built heritage... I have already raised my concern with my staff at the Environment Agency and other officials about the increase in fires at important at-risk buildings this year and we are urgently examining what needs to be done."
Senior fire officer Mark Deeney said: "It was a quite difficult fire to fight. Because of the previous fires, the building was very structurally unsound.
'Access problems'"We have had a minor collapse at the rear of the building overnight because of the previous fire.
"You can also see the fire has spread into the roof area which provides us with problems for access."
It had been hoped to redevelop the 60-acre site which dominates the village.
Celia Ferguson, a member of the Herdman family and a trustee of the Sion Mills Buildings Preservation Trust, said she was "watching the most important industrial building in Ireland being destroyed by fire".
She said it was because of the "neglect of funders to do anything with the building".
She added: "It's a tragedy not just for Sion Mills, but for the whole northwest."
Strabane District Council chairman Brian McMahon said there was a "palpable sense of loss in the local community" at the devastation.
The Sinn Fein councillor, speaking from the scene, said: ""While the full extent of the damage will not become clear for a few days, this fire has undoubtedly delivered a setback in the efforts to redevelop the mill and the 60-acre site it stands on for the socio-economic benefit of the people of this area.
"However, this setback will hopefully reinforce everyone's determination to forge ahead."
Herdman's Mill, the last wet-spinning flax mill in Ireland, was opened during the potato famine.
Police are seeking two men after a woman suffered a serious sexual assault in north Armagh.
As a 'gateway' to the west, the town has suffered from congestion Transport Minister Danny Kennedy has admitted his department does not have the money to build the A4 bypass. 
Nigel Worthington's Northern Ireland will face matches against Russia and Portugal Manager Nigel Worthington believes the World Cup draw has handed Northern Ireland an exciting challenge.
Mr Norris has vowed to continue his presidential campaign despite the problems Irish senator David Norris has vowed to continue his presidential campaign despite admitting his chances of being nominated are "slim". 
Steven Agnew is resigning his seat on North Down Borough Council Green Party MLA Steven Agnew has announced he is stepping down from North Down Borough Council.
The Carvill Group was behind a planned redevelopment of the Sirocco Works site in Belfast One of Northern Ireland's leading property firms owed banks around ?83m when it was placed into administration in May.
The benefits of breast screening are being scrutinised One woman tells BBC News Online how going for a cancer screening saved her life.
Patricia Kearns said her story could have been very different if she had not gone for a screening 
Kildare's Eamonn Callaghan fends off the challenge of Donegal opponent Paddy McGrath Donegal are through to the semi-finals of the All-Ireland Championship after a sensational win over Kildare in Dublin.
Tyrone's Sean Cavanagh goes on the attack as Cathal Cregg of Roscommon attempts to charge the ball down at Croke Park Tyrone will face Dublin in a mouth-watering All-Ireland football quarter-final on 6 August after an 11-point win over Roscommon at Croke Park.
The Fort George site Londonderry's urban regeneration company, Ilex, has confirmed plans to build a cross-border regional science park.
Mr Quinn was knocked down on the Gortgonis Road in Coalisland A man allegedly murdered his second cousin by driving straight at him as the victim raised his arms for the car to stop, the High Court has heard.
A stove like this is saving a lot of money for a Magherafelt businessman We are all feeling the squeeze when it comes to oil and gas prices. 
The US Open champion had a disappointing first round at the Irish Open in Killarney Northern Ireland's US Open champion Rory McIlroy has stumbled into a row on Twitter at the Irish Open in Killarney.
Most of the Superquinn stores are in the Dublin area Irish supermarket chain Superquinn has been bought by the convenience retail group Musgrave. 
'The Birds' represent the display of aerial acrobatics by starlings on the Queen's and Albert bridges The first of 400 patterned banners have been unfurled in Belfast as part of a so-called "city dressing" project.
The City Hall banner 
The officer was shot in the arm while chasing suspects in south Croydon A man charged in connection with the suspected attempted murder of an unarmed police officer in London has no direct link to the shooting, a court in Belfast has been told.
By Debbie Randle
Depression has been an 'ongoing issue' in Northern Ireland There are growing concerns about the suicide rate in Northern Ireland, especially among young men. 
There will be no large increases in university tuition fees for students starting courses in 2012, the first and deputy first ministers have confirmed. 
The alleged attack happened in the grounds of Foyle College on Friday night A 19-year-old man has been charged with raping a teenage girl in Londonderry at the weekend.
Crumlin Star player Anthony Braniff needed stitches after the attack (picture courtesy of Irish News) Members of a north Belfast football team had to be treated in hospital for injuries including stab wounds after they were attacked on the Twelfth.
Five men have been charged over the attack Five men arrested in connection with a gang rape and assault that lasted over 12 hours, had nothing to do with the actual attack, a court has heard.
The case was heard at the High Court in Belfast on Thursday An alleged fraudster conned a newly widowed woman into lending him more than ?7,000 after they met in a Belfast bar, the High Court heard on Thursday.
The UK government said the coastguard service needed to modernise It has emerged that Belfast Coastguard has been saved from closure following a review of UK coastal stations.
Blind supporter Graham Heslip (left), who will open one of Crusaders FC's new stands at the Fulham game, with his father Billy Loyalty in football is often taken for granted, but on Thursday night one Irish League club will show its gratitude to two supporters who have taken their devotion to another level.
The cryptic wood white butterflies have previously been unknown to scientists A new species of butterfly has been found in Northern Ireland. 
Police have been attacked in areas across Northern Ireland in recent days Recent violence in Northern Ireland should make people less complacent about the peace process, the first and deputy first ministers have said.
Clarke's ball-striking was exemplary in the challenging conditions Northern Ireland's Darren Clarke will take a one-shot lead into the final round of the Open at Royal St George's on Sunday.
Johnson's six birdies kept him in contention for the title 
The police helicopter was sent to search for a gunman after a hoax call A PSNI helicopter was sent on a search mission after a Bangor man made a hoax call to say he was going to attack a house with a gun, a court has heard.
The scene of the violence in Portadown 
Police have been attacked with petrol bombs, paint bombs and missiles in Portadown, Belfast and Londonderry.
Down's Kevin McKernan moves clear of Aodhan Gallagher in the qualifier Down scored three second-half goals to easily overcome the Saffrons in the All-Ireland third round qualifier at Casement Park on Saturday night.
Red Sky's Housing Executive contract is now over Maintenance firm Red Sky's contract with the Housing Executive has ended.
Violence has erupted in Belfast in recent days Two men have appeared in court following riots in Belfast on 12 July.
Mr Cairnes is accused of stealing from the Tesco store he managed A former manager of a Tesco supermarket in Limavady is to go on trial charged with stealing just over ?35,000 from his employer. 
Brothers Samuel and Richard Burgess pictured beside the RIB Blue Haven. Photo courtesy of RNLI/Newcastle A Newcastle RNLI lifeboat volunteer lifeboat crewmember and his brother have rescued two children and four adults after their boat sank off the Donegal coast.
Conor Mitchell who died at Craigavon Area Hospital The mother of a disabled child who died in hospital said she is relieved that three charges of misconduct have been upheld against a nurse involved in her son's care.
Jim made the final despite his Mexican restaurant challenge not going well Northern Ireland's contender has negotiated a Mexican stand-off to make it through to the final of the BBC's Apprentice series.
Jamie Clarke fires home his first goal against Wicklow at Aughrim Armagh will face Ulster rivals Tyrone next weekend after Jamie Clarke's double secured victory in the All-Ireland second round qualifier replay.
The Irish justice minister says the priest-penitent confidentially of the confessional is not sacrosanct BBC News Online examines the implications of Irish Justice Minister Alan Shatter's planned legislation to deal with the withholding of information about child abuse. Could it bring the state into direct conflict with the Catholic Church?