Asian shares slipped on Tuesday after a plunge in U.S. manufacturing activity hit American stocks and the dollar, while the euro hovered near a six-week high on optimism over Greece's plan to buy back debt.

MSCI's broadest index of Asia-Pacific shares outside Japan <.MIAPJ0000PUS> fell 0.3 percent to 450.79, backing away from a nine-month high reached on Monday.

Australian shares eased 0.5 percent, while Japan's benchmark Nikkei share average fell 0.2 percent, declining further from a seven-month intraday high of 9,525.82 struck on Monday.

The losses in Asian stock markets were suggestive of some caution after gains in the past few weeks, with some of the negative bias seeping over from weakness in the American economy and continued gridlock in the U.S. Congress over proposals to avert a fiscal cliff - $600 billion worth of tax increases and spending cuts that will be automatically triggered in early 2013.

"Investors are cautious about the market's sharp rise in the past few weeks, and as soon as the Nikkei hit the 9,500-mark, trading has slowed down. Investors started taking a wait-and-see mode," said Hiroichi Nishi, general manager at SMBC Nikko Securities in Tokyo.

Global share indexes had risen on Monday after manufacturing surveys showed signs of a recovery, albeit an uneven one, in China's economy and a slower contraction in Europe. But sentiment toward equities soured after data revealed U.S. manufacturing unexpectedly contracted in November to its lowest level in more than three years.

The Institute for Supply Management (ISM) said on Monday that its index of national factory activity fell to 49.5 in November, the weakest since July 2009, as companies worried about whether lawmakers in Washington could reach a budget deal in time to avert a fiscal crisis that may lead to a recession.

Heading into next week, even a hint of progress in the fiscal cliff negotiations could spawn a modest rally, said Vishnu Varathan, regional economist in Singapore for Mizuho Corporate Bank.

"Overall the euro zone noises are coming out positive and I don't see any turning around there. The only real deal-breaker, whatever will send the dollar spiking up and risk really off the table, will be if there is a complete breakdown in the Congress negotiations," he said.

"Right now there is some disappointment here and there, but overall still the consensus is that negotiations will result in some kind of acceptable compromise," Varathan said.

RBA CUTS

The Australian dollar recovered from initial weakness on Tuesday after a widely expected interest rate cut by the Reserve Bank of Australia (RBA). The rate was trimmed by 25 basis points to 3.0 percent, matching an earlier record low.

The RBA said the full impact of rate cuts in the past had yet to be felt, and that recent data confirmed the peak in resource investment was approaching.

The Aussie rose 0.3 percent on the day and last traded at $1.0445, not far from a two-month peak of $1.0491 touched last week.

The euro was flat at $1.3060, hovering near the previous day's high of $1.3076, the single currency's strongest level in about six weeks.

The euro gained as Greek bonds rallied on Monday after Athens announced better-than-expected terms for its planned debt buy-back, boosting chances it will succeed and lead to the release of fresh aid funds.

European stocks and peripheral bonds were also buoyed by news eurozone finance ministers have approved aid to Spanish banks, alleviating the tail risks of a banking crisis in Spain.

The U.S. fiscal cliff issue remained in the minds of many investors.

The White House dismissed a proposal from congressional Republicans on Monday that included tax reforms and spending cuts, saying it did not meet President Barack Obama's pledge to raise taxes on the wealthiest Americans.

The Republicans proposed overhauling the U.S. tax code to raise $800 billion in new revenue over 10 years. Obama's opening bid, outlined last Friday, seeks $1.6 trillion in new revenue by allowing the expiry of tax cuts enacted under President George W. Bush for the top two tax brackets.

(Additional reporting by Ayai Tomisawa in Tokyo and Vidya Ranganathan in Singapore; Editing by Richard Borsuk)