The NIHE said checks on all 32 high-rise residential accommodation blocks in Northern Ireland were ongoing to ensure they "remain fully compliant with all fire safety regulations".
26% said they tend to support Corbyn's proposal, bringing the total to 59% in agreement.
British authorities are launching a criminal investigation into the London apartment building fire - as the death toll from the blaze has almost doubled, to 30.
Hundreds of protesters also marched on Whitehall, central London, to voice their frustration at the government's response to the fire, which ripped through the tower block in north Kensington on Wednesday morning.
I have heard horrifying stories from the fire brigade, from police and from victims themselves who were in that tower but also from other local residents, some of whom of course have not been able to go back to their homes either. "Would you support or oppose such a move?"
In a brief statement afterwards, a spokesman for the residents said: "We have had two-and-a-half hours with the Prime Minister Theresa May, and spoke about demands and what we expect".
The meeting on Saturday comes amid criticism levelled at Mrs May for not meeting those caught up in the fire in the immediate aftermath of the disaster.
But the Conservative leader still struggled to overcome accusations that she lacked compassion because she had failed to meet with victims on her first visit to the devastated site.
One woman who lived in the flats said she was woken by a frantic neighbour who said a fire had started in his flat. Britain's Press Association says around 70 people are missing.
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The queen marked her official birthday Saturday by saying Britain remains "resolute in the face of adversity" after the horrendous fire and recent extremist attacks in London and Manchester.
Some 19 patients are still being treated in hospital, of whom 10 are in a critical condition, the National Health Service said Saturday.
But when she was asked in an interview on Newsnight on Friday night about whether she had misread the public mood, she sidestepped the question.
London has a chronic housing shortage even in the best of times, and those left homeless by the fire - already angry over what they see as government inequity and incompetence - fear being forced out of the British capital.
"It is hard to escape a very sombre national mood", she said in a message marking the event.
Residents had raised concerns about the fire safety of the building prior to the blaze. Churches and community centers are providing meals and support, and donations of clothing, toys and household supplies are flooding in.
He added: "We would like the chief executive of the council to make public commitments on what the council is going to do for the victims of this borough, and for all the other buildings in the borough that could stand the same fate at Grenfell Towers".
But a report by the Royal Borough of Kensington and Chelsea's Director of Housing just 11 months ago said the tower's safety credentials were exemplary.
Some wore T-shirts with images of missing loved ones as they climbed the front steps and pushed their way into the building.