Mr Bush held talks with Mr Sarkozy and EU Commission head Manuel Barroso
President George W Bush has invited world leaders to gather in the US by the end of the year to discuss reform of the global financial system.
The summit would be the first of a series announced after talks between Mr Bush, French President Nicolas Sarkozy and EU Commission chief Manuel Barroso.
But the agenda is unclear and differences are already emerging.
Mr Bush said any plan must not undermine free markets. Mr Sarkozy said "hateful practices" must be abandoned.
Before he arrived at Camp David, the US presidential retreat in the state of Maryland, the French leader 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
After the meeting, Mr Bush said: "It is essential that we work together because we are in this crisis together."
He went on to invite world leaders to an economic summit after the US election in November, to discuss responses to the current 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 said any plan to rethink financial mechanisms should "preserve the foundations of democratic capitalism" and include "a commitment to free markets, free enterprise and free trade".
Mr Sarkozy 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."
European Commission President Manuel Barroso, who also took part in the talks, said: "We need a new global financial order."
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 of 44 nations after World War II, which established many of the institutions and monetary systems that are now under threat.