John Terrett, Al Jazeera's correspondent in Washington, said: "Bush said to world leaders, 'Look, don't abandon capitalism, its the best way for growth and human justice, and so on.'
"But the talks are limited. We are already hearing that one of the ideas being put forward is an early warning system, in which organisations that we already know - the IMF, the World Bank and others - would spend time surveying the economic system and various financial initiatives and try to ascertain if it's going out of control," he said.
"But how do you know if something is a bubble until it finally bursts?"
The G20 leaders, including leaders of Brazil, India and China, met over dinner on Friday evening before holding several meetings on Saturday.
"The leaders had a good, productive meeting," Dana Perino, the White House spokesman, said.
"The managing director of the IMF, the president of the World Bank, the chairman of the Financial Stability Forum, and the United Nations secretary-general discussed the steps their organisations are taking to address the global financial crisis."
Al Jazeera's Nick Spicer, reporting from Washington, said it may be difficult for the G20 to forge agreements when the US and Europe, not to mention countries such as Brazil and India, have opposing views on regulation and how to deal with the crisis.
"It is hard to come up with a consensus with a lame-duck president in office
who cannot sign off on a new world financial architecture for the American people when he is soon to leave," he said.
Established in 1999 to represent the world's key economies on global financial matters
Its 19 member states, plus the EU, account for 85 per cent of the world economy and two-thirds of its population
Members include both developed and emerging nations that are considered to have strategic economic importance
On Friday the European Commission urged world leaders to prioritise the fight against world poverty during the summit.
"Poverty is the most urgent crisis facing the world," Louis Michel, the EU Development Commissioner, said in a statement.
"The 'Bretton Woods II' summit in Washington offers a crucial opportunity to integrate the development dimension into the new international financial architecture," he said.
Bretton Woods in New Hampshire was the location of a meeting where the World Bank and the International Monetary Fund (IMF) were set up in 1944.
Barack Obama, the US president-elect due to enter office on January 20, is not attending.
The financial crisis began when the US real estate market collapsed as a result of the subprime mortgage crisis, spreading swiftly to the financial sector.
A cash crunch in the banking sector then caused the US credit market to seize up in mid-September, hurting businesses and sending stock markets spiralling downwards.