The debate on the UUP's motion on inclusivity, mutual respect, peace and democracy was delayed by a point of order regarding comments made by Sinn Fein's Alex Maskey about recent violence in the Short Strand area of Belfast, on 15 January 2013.
Paul Givan of the DUP expressed concern that Mr Maskey was not acting within the member's code of conduct with regard to upholding the rule of law and promoting good community relations.
Speaker William Hay told Mr Givan this was a matter for the Standards and Privileges Committee, while Sinn Fein's Gerry Kelly accused Mr Givan of misquoting his party colleague.
Proposing the motion, UUP leader Mike Nesbitt called for "an honest debate and even a passionate debate".
Mr Nesbitt condemned the recent street violence.
"It is all wrong, it has done huge damage to the economy and the public purse," he said.
The party leader called for return to the spirit of the Belfast Agreement.
He said the constitutional question had been settled in 1998, and the recent census had shown "just one in four took the opportunity to call themselves as 'Irish only'."
Gregory Campbell proposed the DUP amendment, which removed the reference to the Belfast Agreement.
He called for members to take on a leadership role and to be direct and honest in their debate.
Mr Campbell laid out some reasons why people were protesting on the streets, including unfair allocation of jobs, the rulings of the Parades Commission, and the promotion of the Irish language above Ulster Scots.
"We have made some progress but we have considerable progress to make," he said.
Mitchel McLaughlin of Sinn Fein said he would speak in favour of the motion and that it was a pity that the amendment removed the reference to the Good Friday Agreement.
He said he now had the power to bring about a united Ireland through persuasion.
"Until that situation arrives I will accept the status quo," he added.
Regarding the flags dispute, the South Antrim MLA said, "Flying the union jack 360 days a year - is that parity of esteem?"
SDLP leader Alasdair McDonnell said it was not enough to talk of the "spirit" of the Good Friday Agreement.
He quoted a section of the agreement regarding equality and parity of esteem.
"How can anyone square that with a winner-takes-all approach to flag-flying?" he added.
Chris Lyttle of Alliance said he had sat with grown women breaking down in tears in the Newtownards Road and Short Strand areas of east Belfast and had assisted them in moving home as a result of the violence.
He said the flags issue had been used by political parties for their own selfish political ends.
Mr Lyttle said the DUP amendment was "wholly unnecessary" and that politicians had fallen short of fulfilling the terms of the Good Friday Agreement.
Paul Givan intervened and said there were lies being told in the chamber. He made reference to the DUP position in Lisburn City Council on the flying of flags.
The speaker warned members about their use of language.
At the beginning of the debate William Hay had informed members that, since a valid petition of concern had been lodged, the vote on the motion would have to be delayed until the next week.
Following a point of order by Mr McLaughlin, the speaker agreed to put it to the Business Committee that standing orders be suspended to allow the vote to be taken the same day.