He said he wanted to "assure our citizens and citizens around the world that this is not the end of the legislative process".
"Our country is not facing a choice between government action and the smooth functioning of the free market," he said.
"We're facing a choice between action and the real prospect of economic hardship for millions of Americans," he warned.
Republican presidential contender John McCain said he was disappointed at the "lack of resolve" shown by both parties in the US House of Representatives.
"The whole spectrum of Main Street America's economy is going to be jeopardised unless we pass this legislation. And we didn't do a good enough job selling it," Mr McCain told US television.
Markets in New York and around the world are having a rough ride
He said he had called Mr Bush on Tuesday, as did his Democratic rival, Barack Obama.
The White House described Mr Bush's conversations with the two presidential candidates as "very constructive".
Mr Obama told a rally of voters in Reno, Nevada: "We must act and act now. We can't have another day like yesterday."
The BBC's Jamie Coomarasamy in Washington says both the president and the two men who hope to succeed him in January are under pressure to show leadership amid the partisan bickering which has followed the bill's failure.
The rivals back the rescue plan, although each has accused the other of contributing towards its collapse.
Republicans and Democrats in Congress are blaming each other over the failed bill, which was rejected by 228 to 205 votes in the House of Representatives on Monday.
Some 133 Republicans and 95 Democrats refused to back the rescue package in a tense vote on the House floor.
On Tuesday, the two leading Democrats in Congress, Senator Harry Reid and House of Representatives Speaker Nancy Pelosi, wrote to President Bush saying they expected a bipartisan rescue plan to soon be approved.
"Working together, we are confident we will pass a responsible bill in the very near future," they said.
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