Hong Kong's blue chip Hang Seng index shed nearly six per cent before it recovered ground and finally closed 0.8 percent up.
India's main stock exchange in Mumbai trimmed sharp early losses and closed 2.1 per cent up at 12,860.43, snapping three consecutive days of losses.
Share prices in Singapore, South Korea and Taiwan all fell sharply on Tuesday before regaining some ground. Australia ended the day down four.
London's FTSE 100 plunged on opening, briefly recovered and oscillated between a loss of three per cent and a gain of 0.77 in morning trades.
Frankfurt's DAX 30 slid 2.19 per cent to 5,679.67 points on opening and in Paris the CAC 40 tumbled 1.96 per cent before recovering to reach 0.26 per cent up at midday.
US stocks had suffered their worst plunge in a single day overnight, with the benchmark Dow Jones industrial index falling 778 points to close at 10,365 after the bail-out bill, aimed at trying to stabilise the US financial sector, was rejected by 228 votes to 205 on Monday.
Massive setback
Al Jazeera's Rosiland Jordan, reporting from Washington DC, said the rejection of the bill was a shocking loss for the Bush administration.
A substantial number of Republicans were saying they did not want the increase in spending and did not believe in any government intervention in the economy, our correspondent said.
George Bush, the US president, said he was "very disappointed" by the rejection of the bail-out and had summoned top aides to plan the next steps.
Nancy Pelosi, the speaker of the house, announced that "the legislation has failed and the crisis is still with us".
"We must work in a bi-partisan way to have another bite at the apple," she said.
The House of Representatives is to reconvene on Thursday over the issue but Republican and Democratic leaders have much to do if they are to persuade their dissenting colleagues to support the bail-out plan.
Blame game
Republicans blamed Pelosi's scathing speech near the close of the debate for the vote's failure.
Pelosi had attacked Bush's economic policies and "right-wing ideology of anything goes, no supervision, no discipline, no regulation".
John Boehner, the Republican house minority leader, said "we could have gotten there today had it not been for the partisan speech that the speaker gave on the floor of the house".
Roy Blunt, the house Republican whip, estimated that Pelosi's speech changed the minds of a dozen Republicans who might otherwise have supported the plan.
That was a remarkable accusation by Republicans against Republicans, said Barney Frank, the Democratic chairman of the house Financial Services Committee.
"Because somebody hurt their feelings, they decided to punish the country," he said.
Gerald Friedman, a US economist, told Al Jazeera the Republicans were to blame.
"The Republicans in the House of Representatives are playing chicken with world economy.
"The pro-deregulation people, the Republicans who voted this down, are the same people who have deregulated financial markets over the last 30 years.
"The people that got us into this mess are now the ones that want to wash their hands of it. It's a little hypocritical."
'Shocking scenes'
Al Jazeera's John Terrett reported that traders had been expecting the bail-out plan to have been voted through before markets opened on Monday.
He said there was shock among those on the floor of the New York Stock Exchanges following news the bail-out plan had been rejected.
Terrett also explained that banks were still not lending to each other - meaning the credit markets were not unfreezing - and the widening international crisis, with banks being rescued on Monday in Germany, Iceland, the UK and Belgium and with New Zealand going into recession, meant fears of a global recession were escalating.
Henry Paulson, the US treasury secretary said US regulators would use "all the tools available" to help the US economy, but he warned their powers were "insufficient" and a rescue plan was urgently needed.
Saying that the rescue plan was "too important to simply let fail", he added: "We need to work as quickly as possible."
Monday's rejection of the bill came despite urgent warnings from Bush and congressional leaders of both parties that the US economy could nosedive into recession, or even a depression, without it.