Asian shares and the euro steadied on Monday on hopes European leaders would agree on a definitive plan to solve the euro zone's debt crisis at a crucial summit this week, with sentiment also getting a lift from Italy unveiling austerity steps.

But investors treaded cautiously were wary of pushing markets much higher at the start of an eventful week, which also sees the European Central Bank's last monetary policy meeting for the year on Thursday, with an expectation for a rate cut.

The market will be playing a tug-of-war this week, with any improvement in sentiment from a political progress in Europe being countered by year-end position-squaring, said Tetsuro Ii, chief executive officer of Commons Asset Management in Tokyo.

He said financial institutions pressured to bolster their core capital would keep selling liquid assets including stocks and bonds, especially after such a sharp rally as last week's.

MSCI's broadest index of Asia Pacific shares outside Japan <.MIAPJ0000PUS> rose as much as 0.3 percent before paring most gains to stand flat. The index ended last week with its first weekly rise in a month, buoyed by joint global central bank liquidity action.

Japan's Nikkei <.N225> gained 0.6 percent and outperformed most other Asian peers on an improved technical outlook, topping its 25-day moving average for the past three sessions. <.T>

U.S. stock index futures also rose, adding to their biggest weekly rally since March 2009 last week after data showing a drop in the U.S. unemployment rate to a 2-1/2-year low reinforced views the economy remained on a recovery path.

Shanghai shares <.SSEC> were down 0.7 percent, weighed by the latest data pointing to a cooling Chinese economy, with the HSBC Purchasing Managers' Index for China's services sector falling to 52.5 from 54.1 in November for its slowest rate of growth in three months.

IMF IN FOCUS

Later on Monday, French President Nicolas Sarkozy and German Chancellor Angela Merkel meet to outline joint proposals for more coercive budget discipline in the euro zone, which they want all 27 EU leaders to approve at Friday's summit.

The focus at the summit will be squarely on new rules to tighten fiscal integration.

An agreement could pave the way for an accelerated implementation of the euro zone's rescue scheme to help ensure debt-ridden countries have a vehicle to tap for funds while encouraging bondholders to buy euro zone bonds.

On Tuesday, U.S. Treasury Secretary Timothy Geithner kicks off his European visit in Germany to meet ECB President Mario Draghi and Germany officials. He will join EU leaders later in the week.

Ii at Commons Asset Management said Geithner's visit raised hopes of further discussion over the International Monetary Fund's involvement in the euro zone debt crisis, as Europe seeks to boost the IMF's resources to enable it to provide a credible backstop should struggling euro zone borrowers need an emergency loan programme.

In a further sign Europe is making progress, four sources have told Reuters Germany is prepared to soften language in the euro zone's permanent bailout mechanism compelling bondholders to accept losses in exchange for much stricter budget rules.

Italy, one of the most severely debt-stricken euro zone countries which has faced soaring borrowing costs, unveiled a 30-billion-euro ($40.3 billion) package of austerity measures on Sunday, raising taxes and increasing the pension age.

The euro climbed as high as $1.3435 on Italy's news, but was last at $1.3410, up marginally from late in New York.

The euro may find some support due to the potential for short-covering, a trader for a Japanese bank said, as latest U.S. CFTC data showed currency speculators increased their net short position in the euro to 104,302 contracts in the week ended November 29 from 85,068 contracts a week earlier.

Traders who are short have sold a currency in a bet that it will fall, but when they buy it back to cover their position and realise the gain it can often provide a short-term lift.

Last week's coordinated move by major global central banks aimed at reducing dollar funding costs eased tension in the immediate aftermath, but financial stresses returned by Friday.

The three-month euro/dollar cross currency basis swap, which narrowed sharply after the central bank move, widened again on Friday. The London interbank offered rates for three-month dollars inched up on Friday after falling for the first time in more than four months after the central bank action.

Investor confidence recovered in Asian credit markets, with spreads on the iTraxx Asia ex-Japan investment grade index tightening by 7 basis points on Monday.

(Additional reporting by Masayuki Kitano in Singapore; Editing by Alex Richardson)