The pair were immediately accused of “patting each other on the back” instead of addressing the country’s needs.
The Prime Minister admitted questions had been raised about the future of the partnership in the wake of the Tory rebellion last week over House of Lords reform.
But he said there was a “huge momentum” in the Government to rebalance the economy and education reforms.
He said: “I just want to say I am even more committed to coalition government, to making this coalition government, today than I was in May 2010 when Nick Clegg and I formed this government.
“I believe it has real purpose, a real mission.”
Mr Clegg dismissed the Lords row as one of the “bumps in the road” to be expected in the circumstances, especially on an issue which excited strong opinions among politicians.
But despite disagreements between the two parties, he added: “None of that will stop us from continuing to govern in the national interest for the country.”
The men sought to draw a line under angry exchanges between the two parties in the wake of last week’s Tory revolt which threatens to derail Mr Clegg’s plans for House of Lords reform.
Despite a weekend appeal by Mr Cameron to put aside “division and navel-gazing”, senior figures on each side engaged in sniping over the future of the power-sharing administration.
Echoing the Prime Minister’s message about the coalition being stronger now than in 2010, Mr Clegg acknowledged that they disagreed on some issues.
“We are two different parties: he doesn’t agree with all my opinions and I don’t agree with all his opinions. That’s coalition government.
“It’s tough also to be in government in difficult times. It is not always a walk in the park or in the rose garden,” he said in a reference to the first such joint news conference.
“You also get some bumps in the road in the Westminster village as we did last week on House of Lords reform.
“House of Lords reform so happens to be one of those things that gets politicians really hot under the collar in the Westminster village, particularly those who are opposed to change.
“It always has done and I imagine it always will. But none of that will stop us from continuing to govern in the national interest for the whole country.
“Above all that means accepting that there are no simple, quick, easy short cuts which secure instant political popularity.
“We need to put short-term popularity to one side and get on with making the big long-term reforms and changes that this country so desperately needs,” he said – identifying those areas as economic and social renewal.
Mr Cameron said that in two years there had been only “one or two episodes like last week” and that the major revolt did not reflect deeper problems within the coalition.
“You always have bumps and scrapes and difficulties along the way. That is the nature of politics,” he said in response to questions.
“With the House of Lords you always have to be frank: there are people on both sides of the argument, people of principle. Some of them have held their views either for or against having elected members for a very long time.
“So I do not take that as an indicator of the health of the Government or its momentum or its purpose. I think it has real purpose, real momentum and that is what we are committed to driving forward in the years ahead.”
There was “much more to come” on the shared agenda, he said, and promised a “mid-term review” would be published later in the summer.
Over the weekend, Mr Cameron urged Conservatives and Liberal Democrats to come together behind the coalition and not to descend into “division and navel-gazing”.
Michael Dugher MP, Labour’s Shadow Minister without Portfolio, said: “The sight of David Cameron and Nick Clegg congratulating themselves on their ‘success’ at a time when they’ve delivered a double dip recession made in Downing Street shows how out of touch they are. What planet are they living on?
“Cameron and Clegg’s time would be better spent addressing the needs of the country, rather than patting each other on the back at press conferences.”
The appearance of Mr Cameron and Mr Clegg at the press conference failed to halt the angry exchanges over Lords reform.
Former Lib Dem leader Sir Menzies Campbell warned that his party’s MPs may refuse to back Conservative plans to redraw parliamentary boundaries – thought to be worth an extra 20 seats to the Tories at the next general election – unless Lords reform goes ahead.
On the Conservative side, the chairman of the Tory backbench 1922 Committee, Graham Brady, said he believed the coalition was now “very likely” to come to an end before the general election, set for 2015.
They seek the coalition here they seek them there oh dear here comes Hurricane Johnson the mayor of London to put his spin on it yeah the coalition is splitting .
Let’s remember that the coalition may not like each other but they have a job to do and as I said in my previous communications they are in it for the long term. Don’t be hoodwinked by what the media says if Cleggy Babes does not get his wish of having the House of Reform then the Fibdems will revolt that is a load of pfui if anything it’s the Tory rebels that will to the damage.
Coalition has the cheek to say that we are all in it together I say to both voters and politicians to run as far as you can as the voters are already angry with the coalition Fibdems they have broken their promises over tuition fees, and welfare state. In the Caribbean there is a saying “A promise is a comfort to a fool”.
Labour is taking the lead in the opinion polls but I say exercise cation with the figures as what goes up must come down. Why is Labour in a better position to remain where they are. They will see the coalition dig their own graves then the coalition will always say its Red Ed fault and Labour listens to the Trade Unions their pay master.
Coming back to why I don’t believe anything that Boris Johnson has to say is simple he play’s the media to score points to get his message across to them by saying I told you so. In other words I need to promote myself to the leadership of the Conservatives Party.
However, Boris should not be underestimated he is just waiting for the right time when the coalition can’t get any worse then he will become the prince of darkness to take other the leadership with little opposition.
Boris Johnson has said the coalition government will last to 2015, telling the BBC it was “doomed to succeed”.
The Mayor of London said there was “no reason” for the Conservative and Liberal Democrats to go their separate ways before then.
Some Conservative MPs have been speculating that the arrangement will break up well before the scheduled date of the next election in May 2015.
This follows tensions over reforms to the House of Lords and other issues.
‘Moment of separation’
The largest rebellion in the coalition’ s history over plans for a mainly elected Lords – in which more than 90 Conservative MPs voted against their leadership – has prompted fresh speculation about the government’s longevity.
It is always possible that that moment of separation could come sooner”
End Quote Graham Brady Conservative MP
Mr Cameron has acknowledged “profound areas of disagreement” between the two parties, but told the Sunday Times they must work together in the national interest over the next few years.
Asked about the coalition’ s future, Mr Johnson told BBC Breakfast that “logically it must be true that at some stage by 2015 there will have to be a decision to part company and to campaign on a different prospectus”.
He added: “But I don’t see any need particularly for it to happen urgently.
“It is a marriage which is doomed to succeed. It will continue absolutely until the last moment when it is necessary to part in order for two parties to go into two campaigns on separate manifestos.”
On Sunday a senior Conservative backbencher said it was “very likely” the coalition would end before the start of the next general election campaign.
“I think it would be logical and sensible for both parties to be able to present their separate vision to the public in time for the public to form a clear view before the election,” Graham Brady, chair of the influential 1922 backbench committee, told BBC Radio 4’s The Westminster Hour.
“Of course, it is always possible that that moment of separation could come sooner. It’s very difficult to predict when that might be.”
Senior Tories, including the former defence secretary Liam Fox, have accused the Lib Dems of sidetracking the government over Lords reform and have urged Mr Cameron to assert his authority on key issues like the economy, Europe and welfare.
But former Lib Dem leader Sir Menzies Campbell has said the coalition was a “marriage of inconvenience”.
He has suggested many Lib Dem MPs would find it “hard to swallow” proposed changes to Commons constituency boundaries in 2015 – thought to favour Conservative chances of getting a future majority – if changes to the House of Lords do not proceed.
Mr Cameron and Mr Clegg were fully committed to the coalition and neither wanted an early election. This a code word for Lets get on with it and let’s see who dares to struggle and dare to win.
The leaders’ immediate task, he added, was to “calm their parties” down after recent events and demonstrate their focus on the economy and getting the UK out of recession as quickly as possible.