A massive relief rally in world stocks on news of a $1 trillion deal to resolve Europe's debt crisis slowed down on Tuesday in Asia on nagging doubts about how Greece and other debt-laden euro zone countries will reduce their budget deficits.

The euro, which had initially surged on the news of the package put together by EU finance ministers, central bankers and the IMF, was slightly weaker on Tuesday and well off its Monday high.

The European rescue package, together with a pledge from the European Central Bank to buy government bonds, helped ease worries about the risk of contagion from Greece's debt crisis.

In response, markets soared worldwide on Monday. Stocks in fiscally weak Greece, Spain and Portugal jumped by double digits and the risk premiums on their debt tumbled against benchmark German bunds. Wall Street racked up its biggest one-day gain in over a year.

But longer-term concerns remained over whether Greece and some other euro zone countries with large fiscal deficits will be able to smoothly carry out fiscal austerity measures, market players said.

Those worries capped the upside for Asian equities.

MSCI's index of Asia-Pacific shares outside Japan rose 0.5 percent <.MIAPJ0000PUS> after climbing 3.4 percent on Monday for its biggest single-day percentage gain since May 2009.

Japan's Nikkei average <.N225>, which gained 1.6 percent on Monday, rose 0.3 percent on Tuesday. South Korean shares <.KS11>, which pushed 1.8 percent higher on Monday, edged up 0.5 percent.

Tokyo markets already had a chance to respond to this news yesterday and basically have now settled down, said Nagayuki Yamagishi, a strategist at Mitsubishi UFJ Morgan Stanley Securities.

Besides, even though one of the worst scenarios -- a Greek default -- has been avoided for now, in many ways solving the bigger problems have simply been postponed and new issues could emerge in places such as Portugal and Spain.

The euro edged marginally lower to $1.2770 compared with late U.S. trading on Monday and slipped against the yen.

The single European currency has rebounded from a 14-month trough of $1.2510 hit last week on trading platform EBS when markets slumped on concerns that the euro area was doing too little to try to prevent the risk of contagion.

But the euro was well off its Monday high near $1.3100, having retreated back close to where it was late last week before the European Union's emergency package was unveiled.

The emergency package is likely to ask Greece to adopt very demanding steps to cut its debt, leaving us with doubts over whether it will be able to implement such budget reform, said Tsutomu Soma, senior manager of the foreign securities department at Okasan Securities.

The emergency package is effective in avoiding a near-term crisis. But so much uncertainty remains for the euro zone.

Sterling held steady at $1.4856, but was held back by political uncertainty in Britain following an election last Thursday that left no single party with a clear majority to rule.

Prime Minister Gordon Brown said he would step down in an effort to try to keep his Labour Party in power. Labour and its major rival, the Conservatives, are trying to woo the smaller Liberal Democrats to gather enough seats to form a government.

U.S. crude futures rose 0.6% to above $77 a barrel and spot gold was little changed at $1,202.70 an ounce.

(Additional reporting by Elaine Lies, Rika Otsuka and Kaori Kaneko; Editing by Neil Fullick)

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