The planned summits will "seek agreement on principles of reform"
The presidents of the US, France and the European Commission have unveiled plans for a series of summits to discuss the global financial crisis.
Speaking before talks at Camp David with Nicolas Sarkozy and Jose Manuel Barroso, George W Bush said it was "essential that we work together".
The first summit will be held in the US after November's presidential election.
The Europeans want the meetings to pave the way for talks on an overhaul of the world's financial regulatory systems.
Before he arrived at Camp David, the presidential retreat in the state of Maryland, Mr Sarkozy warned the world could not "continue to run the economy of the 21st Century with instruments of the economy of the 20th Century".
Calls for action
The BBC's Adam Brookes in Washington says that against the beautiful autumnal backdrop of the retreat, Mr Bush uttered words of cold comfort to his French counterpart and Mr Barroso.
Together we will work to modernise and strengthen our nations' financial systems so we can help ensure this crisis doesn't happen again
US President George W Bush
"It is essential that we work together because we are in this crisis together," he said.
Mr Bush went on to invite world leaders to a global economic summit in the US soon to talk about the global response to the financial crisis.
"Together we will work to modernise and strengthen our nations' financial systems so we can help ensure this crisis doesn't happen again," he added.
But Mr Bush asserted that any plan to re-think the mechanisms of the global financial system could not be allowed to undermine the free market.
"It is essential that we preserve the foundations of democratic capitalism - a commitment to free markets, free enterprise and free trade," he said.
President Sarkozy seemed to have a rather more sweeping vision to deal with what he called a "worldwide crisis", our correspondent says.
He said the crisis could offer a "great opportunity" to build the capitalism of the future and leave behind the "hateful practices" of the past.
"We cannot continue along the same lines because the same problems will trigger the same disasters," he warned.
Mr Sarkozy said the hedge funds, tax havens and financial institutions operating without supervision should all be re-thought.
"This is no longer acceptable," he added. "This sort of capitalism is a betrayal of the sort of capitalism we believe in."
Mr Barroso said European nations had taken swift action to tackle the squeeze in the financial markets, but stronger and more effective global action was now required.
"We need a new global financial order," he added.
Details of the summits are still to be worked out, but White House spokesman Tony Fratto said the first was likely to be held in November.
He added that Mr Sarkozy had recommended New York as a location. UN Secretary General Ban Ki-moon has proposed using the organisation's headquarters there as a venue.
A global summit would echo the Bretton Woods conference in 1944
That summit would seek to "review progress being made to address the current crisis and to seek agreement on principles of reform needed to avoid a repetition," the leaders said in their statement.
"Later summits would be designed to implement agreement on specific steps to be taken to meet those principles," it added. Other world leaders are to be consulted over the plan.
Correspondents say such meetings would echo the Bretton Woods conference after World War II.
At Bretton Woods, world leaders agreed to establish the International Monetary Fund and the International Bank for Reconstruction and Development, the original institution of the World Bank Group, in an effort to prevent a repeat of the depression of the 1930s.
'Big enough and bold enough'
Earlier on Saturday, in his weekly radio address, Mr Bush sought once again to reassure Americans about the $700bn bail-out of US financial institutions.
Elements of the plan are similar to those earlier announced by European governments.
The president said the federal government had taken "aggressive measures" to protect financial security.
The BBC's Jane O'Brien in Washington says European leaders have in the past blamed the US for the crisis, which started when borrowers began defaulting on their mortgages.
But she adds that Mr Sarkozy, whose country currently holds the EU presidency, has made it clear he wants to move away from finger-pointing and towards a partnership with the US.