* Oil climbs to around $99 a barrel after slide
* Europe rescues more banks; US, European shares rise
* Bush urges Congress to act on $700 billion bailout (Recasts, updates prices, market activity, changes dateline, previous LONDON)
NEW YORK, Sept 30 (Reuters) - Oil over $2 firmer on Tuesday, trading at around $99 a barrel, after a fall of almost 10 percent in the previous session, as fears of a major meltdown in financial markets eased.
U.S. crude <CLc1> was up $2.64 at $99.01 a barrel by 12:08 p.m. EDT (1608 GMT), after losing $10.52 on Monday to $96.37 -- the second biggest fall since April 23, 2003. London Brent crude <LCOc1> rose $2.46 to $96.44.
U.S. shares <
> rebounded after Wall Street's worst day in 20 years, while European stocks < > set new highs for the day.The rebound suggested markets had fallen too far in Monday's selloff after the U.S. Congress rejected a $700 billion financial sector rescue plan.
"We've been moving in tandem with how the equity markets have performed," said Rob Laughlin of MF Global. "In terms of the rally today, I think things were overdone last night across many markets, including energy."
"I'm not suggesting the panic is over but I am suggesting the scare tactics in some quarters have proven to be rather overdone."
CRITICAL MOMENT
The U.S. House of Representatives on Monday voted 228 to 205 against a bailout plan that would have allowed the Treasury to buy up toxic assets from banks. The unexpected rejection of the plan sent stock markets sliding.
U.S. President George W. Bush said this was not the end of the legislative process on the plan.
"We're at a critical moment for our economy and we need legislation that addresses the troubled assets," he told reporters at the White House. "Congress must act."
More evidence of distress in the financial sector emerged, with Belgian-French financial services group Dexia <DEXI.BR> getting a 6.4 billion euro ($9.18 billion) capital boost from public shareholders.
Ireland offered to guarantee all bank deposits for two years to improve banks' access to funds on international markets, helping sentiment in the equity market.
Oil has fallen sharply from a record high of $147.27 reached in July on signs that high energy prices and the financial crisis have cut into crude demand in the United States and other industrialised nations.
In addition, oil has also been dragged down as investors, who had rushed into commodities earlier this year as a hedge against inflation and the weak dollar, sold crude for safer havens.
Analysts said the spread of credit problems to Europe was stoking fears the financial turmoil, which started with risky lending to the U.S. property market, had gone global rapidly.
"Slower international economic growth is bound to dent oil demand," said David Moore, a commodities analyst at the Commonwealth Bank of Australia. (Reporting by Rebekah Kebede in New York, Alex Lawler and Jane Merrimanin Londen, additional reporting by Maryelle Demongeot in Singapore and Fayen Wong in Perth; Editing by David Gregorio)