David Cameron has said the coalition government remains "very strong" despite recent tensions over Europe.
After chairing a cabinet meeting, the prime minister said the coalition existed for a "good reason" - to tackle the challenges facing the UK.
And Lib Dem leader Nick Clegg told his MPs that although the UK needed to "build bridges" in Europe the coalition would last "full stop".
But Lib Dems later declined to support the government in a vote over Europe.
Lib Dem MPs abstained en masse on a motion put forward by the Democratic Unionist Party commending the prime minister's actions in opposing changes to EU treaties but the Commons still backed the government by 278 to 200.
Although largely symbolic, the vote was the first indication of Parliament's views since the outcome of Friday's summit.
Amid the continuing fallout over how the UK came to use its veto, Lib Dem energy secretary Chris Huhne said the UK had been left isolated and "playing Billy no-mates is not fun and not effective in promoting Britain's interests".
However, Mr Cameron struck an upbeat tone after Tuesday's Cabinet meeting - the first since the EU summit.
"The coalition is very strong," the prime minister said. "The coalition came together for a good reason, which was to put aside party interest and to act in the national interest particularly while there are so many challenges facing our economy.
"We had a very good cabinet meeting this morning where we talked about those challenges, we talked about the issues of recent days, and I think the coalition will come out of this very strongly."
Leaving the meeting, Lib Dem Business Secretary Vince Cable said the atmosphere at cabinet had been "business-like".
And deputy prime minister Nick Clegg told a meeting of MPs later on Tuesday that "this government carries on until 2015, full stop".
Mr Clegg's absence from the Commons on Monday was one of the main talking points after the prime minister fielded questions from MPs about his reasons for using the UK's veto to block EU-wide treaty changes designed to facilitate closer union between eurozone members.
Afterwards Mr Clegg said he "would have been a distraction" if he was there but several Conservative MPs criticised his decision to stay away, one accusing him of "cowardice", while Labour said it was evidence that the government was irreparably divided over Europe.
But BBC political correspondent Carole Walker said sources suggested everyone who contributed at Tuesday's meeting spoke of the need for the coalition not to break up but for the Lib Dems also to pursue a policy of constructive engagement in Europe.
MPs debated the issue of Europe in the House of Commons and backed a motion by the Democratic Unionists commending Mr Cameron's use of the veto as a "vital means" of protecting the UK's interests by 278 votes to 200.
"It is time we realised in this House that focusing our foreign policy on the narrow ground of 'greater Europeanism' and ever closer political union in Europe is actually contrary to the UK's vital interests," Nigel Dodds, the party's leader in Westminster, said.
"For too long our vision as a country has been dominated by the 'little Europeanists' who only want to take us in one direction and it is high time this blinkered approach is discarded."
Recent events had "brought the day closer" when the public had to have their say on the UK's role in the EU in a referendum, Mr Dodds claimed.
Labour, who opposed the motion, said the prime minister had been driven by party political considerations and had not secured any additional safeguards for the City, but this was not chosen for debate.
Downing Street have rejected suggestions by the European Commission president Jose Manuel Barroso that the UK's negotiating position on financial regulation represented a "risk to the integrity of the single market".
A No 10 spokesman said it was not the UK's intention to "undermine the single market in any way" and said it had been seeking equal, not preferential, status for the City of London in negotiations over financial regulation.
Estonian Prime Minister Andrus Ansip, one of those to sign up to new rules on fiscal discipline and budgetary oversight, told the BBC he was not "angry" with the UK's refusal to do so, as each country had the right to pursue its own interests.
But he said the euro had been "beneficial" for his country and he believed eurozone members should have the right to use the resources of institutions such as the European Commission and the European Court of Justice to help them work closer together.