Asian shares dipped Tuesday after U.S. manufacturing activity hit a three-year low in November, while the euro hovered near a six-week high on optimism over a planned Greek debt buyback.

MSCI's broadest index of Asia-Pacific shares outside Japan eased 0.2 percent to 451.27, backing away from a nine-month high struck on Monday, Reuters reported.

Australian shares eased 0.3 percent, while Japan's Nikkei sagged 0.3 percent, from a seven-month intraday high of 9,525.82 struck on Monday.

"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,"  Hiroichi Nishi, general manager at SMBC Nikko Securities in Tokyo, told Reuters.

Sentiment for equities was dampened after U.S. manufacturing unexpectedly contracted in November to its lowest level in more than three years.

The Institute for Supply Management said 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 crisis that many lead to a recession.

The euro eased 0.1 percent to $1.3048, hovering near the previous day's high of $1.3076, the single currency's strongest level in about six weeks.

The euro gained a lift 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.

The Australian dollar held steady from late U.S. trade on Monday at $1.0421 ahead of an interest rate decision by Australia's central bank later on Tuesday.

Market expectations are for the Reserve Bank of Australia to cut interest rates by 25 basis points to 3.0 percent, matching an earlier record low, when it announces its decision at 0330 GMT.

Asian shares had touched a nine-month peak on Monday as further signs of a stabilizing Chinese economy boosted investor risk appetite.