Wall Street rallied on Tuesday as investors bet Washington would revive a plan to stabilize the financial sector.
The markets on Monday had their worst sell-off in 21 years, after the US House of Representatives voted against a $US700 billion bailout, by 228-205 votes.
The Dow Jones industrial average plunged by a record 777 points on Monday.
However, the Dow rallied 485.21 points, or 4.68%, to 10,850.66 on Tuesday as the market recouped more than half the losses from the previous day.
Standard & Poor's 500 Index jumped 58.35 points, or 5.27 percent, to 1,164.74. The Nasdaq Composite Index climbed 98.60 points, or 4.97%, to 2,082.33.
The Nasdaq fell more than 9% on Monday.
About 1.62 billion shares changed hands on the New York Stock Exchange - below last year's estimated daily average of roughly 1.90 billion.
About 2.37 billion shares were traded on the Nasdaq - well above last year's daily average of 2.17 billion.
For the month of September, the Dow fell 6% - its worst month since June.
For the September quarter, the Dow fell 4.4% while the Nasdaq fell 9.2%.
The FTSEurofirst index of leading European shares ended up 1.59% at 1,063.65 on Tuesday.
In London, the FTSE 100 index of leading shares finished with a gain of 1.74% at 4,902.45 points.
The Paris CAC 40 rose 1.99% to 4.032.10 points and Frankfurt's DAX added 0.41% to 5,831.02 points.
Dealers said the hope was that the US rescue plan will eventually get through.
But global money markets remained frozen, and London interbank offered rates shot to record levels, indicating banks were not lending to each other.
The rate for overnight dollar loans rose to nearly 6.9% from just over 2.5% on Monday.
Meanwhile, Dexia became the latest European bank to need a state bailout with Belgium, France and Luxembourg investing 6.4 billion euros into the group.
Ireland has announced a blanket guarantee for savings held by six banks and building societies for two years, covering up to 400 billion euros in liabilities.
President George Bush has warned lawmakers opposed to the bailout plan that the threat to the US economy "will grow worse each day" that goes by without a deal.
He said that action had to be taken.
Congress was not in session on Tuesday because of the Jewish holiday of Rosh Hashanah.
The Senate could take up bailout legislation again as early as Wednesday. The House is due to return on Thursday.
A number of those who helped defeat the bailout are up for reelection on 4 November.