Mr Gerry Adams said Sinn Fein would abstain on the vote to elect a First Minister and Deputy First Minister but that the party accepted "the entitlement and the right of the largest party" to hold the top job and for the SDLP to hold the No 2 position.
He said he believed it would be "useful" for the two parties to rotate the position because the difference between them in the election was so narrow.
He began his address to the Assembly in Irish, prompting taunts from the DUP. Lord Alderdice called for order, and, to laughter from his party colleagues, the Rev Ian Paisley replied: "If we could understand him, we might listen."
In explaining his party's decision to abstain in the vote, Mr Adams said Sinn Fein had tried to be far-sighted and strategic about the changes in unionism.
"We consider we may not be doing Mr Trimble any favour by voting for him," he said, adding that other unionists would use this against Mr Trimble.
He said that in upholding the UUP entitlement, he hoped the Ulster Unionists would uphold Sinn Fein's entitlement.
He said there was a lot of work to be done and a lot of change to be brought about, "not just in this institution, but in cross-Border bodies, and in the Council of Ministers".
Mr Adams said he wished everyone well. "It is only by meeting like this that we will work out a shared future for all the people of this island."
Earlier the deputy leader of the Ulster Unionist Party, Mr John Taylor, nominated Mr David Trimble and Mr Seamus Mallon for the positions of First Minister and Deputy First Minister.
He said: "We have to take Northern Ireland out of the morass it has been in for the past 30 years so that Northern Ireland can hold its head high, not only here in the United Kingdom, but in Europe, the US and among our neighbours."
He said Mr Trimble had shown "the leadership and vision we've needed to reach the stage we are at today". He added that although he and Mr Mallon "disagree strongly on our political objectives, I found him a man who is a good friend, and one who will work for the good of Northern Ireland".
The SDLP leader, Mr John Hume, seconded the proposal. He said it "symbolises the fundamental objective of this institution" that the representatives of both sections of the community would work together in the best interests of all sections of the community.
Some of the most heated exchanges of the opening debate came when Mr Martin McGuinness of Sinn Fein was speaking.
He accused the UK Unionist leader, Mr Robert McCartney, of trying to intimidate pro-agreement unionists. Mr McCartney retorted: "Don't talk to me about intimidation" and shouted "Gunman!" at Mr McGuinness.
Mr McGuinness said there was nothing in the agreement to deny Sinn Fein its places in the executive of the Assembly, and said that while anti-agreement unionists would try to block change, by their involvement in the Assembly they would be a part of the change that would take place.
He then criticised the Rev Ian Paisley and the DUP, saying it was time "to discard the maroon berets, the Ulster Resistance and the tons of arms that were brought in from South Africa."
Mr McCartney said UUP members had a duty to exercise their conscience, and ask if they could accept their leader sitting in government with "Sinn Fein/IRA".
The DUP and members of the UK Unionist Party repeatedly attacked Sinn Fein over IRA violence.
Dr Paisley said he was thinking of "the people turned into vegetables by IRA violence", in opposing Sinn Fein members taking executive positions.