Jeremy Corbyn has pledged to extend same-sex marriage and the 1967 Abortion Act to Northern Ireland, and will reverse the DUP-backed gay blood ban if he becomes Prime Minister.
He would also reverse welfare cuts, and would convene new talks on benefits here if he becomes PM.
The left-wing MP - the current favourite in the UK Labour leadership race - was speaking at the West Belfast Talks Back panel discussion at Feile an Phobail.
Earlier, he had avoided questions on the BBC's Nolan Show about whether he condemned IRA terrorism. Stephen Nolan asked him repeatedly if he was prepared to condemn IRA violence and also if he considered the IRA equivalent to the British Army.
At the time of the radio interview, Mr Corbyn was on a train and announcements were being made in the background. At first he fielded the question of the IRA campaign. He said: "Can I answer the question in this way? We gained ceasefires, they were important and a huge step forward. Those ceasefires brought about the peace process, brought about the reconciliation process which we should all be pleased about. Can we take the thing forward rather than backward?"
When Mr Nolan pressed him to answer the question he at first said he couldn't hear. Then, when the noise stopped and Mr Nolan repeated the question the line went dead.
Last night, Mr Corbyn avoided journalists in west Belfast. This reporter was shown out of a reception by festival security while waiting for Mr Corbyn after he had promised to speak.
Before the meeting he spoke only to Will Leitch of the BBC. Mr Leitch asked him if he wanted to be the Prime Minister of Northern Ireland, a reference to his support for Irish unity.
Mr Corbyn responded: "Northern Ireland has come through the most amazing transformation. The peace process has come about, we have devolved government in Northern Ireland, it is up to the people in Northern Ireland and Ireland as a whole to decide what the long term future is. It is not up to me to dictate that."
On the question of victims, he clashed with panel member Gavin Robinson, the DUP MP for East Belfast. Mr Robinson said that in terms of compensation "victims" could be supported but not "victim makers". Mr Corbyn said that "anyone can be a victim".
One member of the Labour Party in Northern Ireland, which has nearly 500 members, asked him if he would support the extension of a number of "equality issues" to the province, including abortion, same-sex marriage and the right to stand candidates here. Mr Corbyn said he would "support the extension of all UK equality legislation to Northern Ireland".
He said he was open to discussion on Labour standing here, but was personally opposed to the idea. In contrast, Mr Robinson was opposed to same sex marriage and abortion legislation but supported Labour standing here.
Ann Travers, who lost her 22-year-old sister to IRA killers in 1984, said she was shocked that Mr Corbyn declined to give an outright condemnation of IRA activities and said it amounted to an "insult to all our dead loved ones". "I am shocked and disappointed that an MP, especially someone who hopes to win a leadership contest and lead the Labour Party into government, would find it so difficult to say five simple words, 'Yes I condemn the IRA'. Terrorism destroyed our country, terrorism from all sides, it achieved nothing, only broken hearts and broken dreams.
"Any right-minded, moral, government minister shouldn't have to think twice to condemn it."
Colin Wharton, whose brother Kenneth was killed in the Kingsmills massacre in 1976, added: "I would be concerned at someone of his stature being the leader of the Labour Party."
Colin Parry - whose 12-year-old son Tim was killed in an IRA bomb in the centre of Warrington near Manchester in 1993 - expressed doubt that Mr Corbyn could win a general election for Labour.
"When I saw the nature of the interview it didn't surprise me," he said. "I think he saw an equivalence between the British Government's armed forces and republican terrorists which I think anyone with a balanced view in Northern Ireland could hardly agree with."
Stephen Nolan quotes the Daily Telegraph in June. "This is a man who sympathised with violent Irish republicanism in the 80s, invited IRA representatives to the Commons a fortnight after the Brighton bombing in 1984 and at a Troops Out meeting in 1987 he stood for a moment's silence for eight IRA terrorists killed in an SAS ambush". How do you respond to that.