The First Minister and Deputy First Minister are united in their resolve to protect the power-sharing Assembly, Mr Seamus Mallon said.
Mr Mallon and Mr Trimble sat side by side in the Assembly for question time and the DUP's Mr Sammy Wilson said he was glad to see "they had kissed and made up".
To laughter from Assembly members, especially those on the anti-agreement unionist benches, Mr Mallon said he was glad Mr Wilson "recognises that the First Minister and I have a very good personal relationship.
"I am also glad that he recognises that within any political process, there will be divergences of opinion but the strength of any political process is that those divergences are overcome and I can assure the Assemblyman that the First Minister and I will do everything we can to ensure that the institutions we are involved in and have responsibility for will proceed."
The presiding officer said he would investigate "whether kissing and making up is parliamentary or unparliamentary behaviour".
Questioned by the DUP's Mr Edwin Poots, and Sinn Fein's Mr Alex Maskey as to whether Sinn Fein Ministers would be permitted to attend the next meeting of the British-Irish Council, Mr Mallon said both he and the First Minister would make nominations "as usual".
The Deputy First Minister said they would bring the nominations for the meeting, due to take place on November 20th in Dublin, to the Executive and the Assembly. "Those nominations will be made on the basis of equity," he said.
The Minister of Health, Ms Bairbre de Brun, defended herself against an accusation of wasting the price of two hip replacements - about £6,000 - on a "nationalist junket" with the Minister for Health, Mr Martin.
Ms de Brun met Mr Martin in Enniskillen on Friday after the First Minister refused to nominate her for a planned meeting of the North-South Ministerial Council.
She was answering questions on the new all-Ireland Food Standards Agency which, she said, would provide clear and timely advice on all food-related matters.
Mr Ian Paisley jnr of the DUP asked, "Is this the best use of resources by the Minister?"
Ms de Brun replied that, in her view, "it was a very, very worthwhile use of resources which will lead to considerable, tangible benefits on food safety and health throughout the island of Ireland".
In other business, a Bill enabling the courts to use DNA testing to determine the parentage of a child passed its second stage. The Family Law Bill also recognises the right of unmarried registered fathers to exercise parental responsibilities for their children.
Prof Monica McWilliams of the Women's Coalition, urged the Assembly to make the public aware of the legislation and publicise the Finance and Personnel Committee's session to consider the Bill.
Meanwhile, a study on climate change will be commissioned, the Minister of the Environment, Mr Sam Foster, told the Assembly. The Minister said the study would focus on water resources, flood protection, buildings, habitats and land-use planning.