The dollar inched up on Tuesday, boosted by strong U.S. data indicating the world's largest economy was on the mend, but worries about Greece's bailout and China's policy tightening curbed earlier gain in Asian shares.

The dollar firmed against a basket of major currencies, and hovered near 8-½ month highs against the yen while the euro huddled near one-year lows.

The euro is heading toward lower lows, said John Horner, currency strategist at Deutsche Bank.

It's a combination of good U.S. data and a general feeling that the political process in the euro zone in trying to solve the Greek crisis is cumbersome that is hurting sentiment.

U.S. factory activity grew at the fastest pace in nearly six years and an unexpected rise in construction spending lifted the main U.S. stock indices between 1.3 and 1.5 percent higher on Monday.

The MSCI index of Asian shares outside Japan initially rose reacting to the U.S. data and gains on Wall Street, but later pulled back. It was 0.06 percent <.MIAPJ0000PUS> lower as of 0327 GMT.

China's key stock index <.SSEC> fell to a seven-month low as investors reacted to the latest policy tightening by the central bank following a market holiday on Monday.

On Sunday the central bank said it would raise the amount of money banks need to keep in reserves, the third such increase this year in a campaign to absorb excess cash in the economy and stem inflation.

The decision is seen as a possible precursor to an interest rate hike.

Data from the United States, the largest export market for Asia, helped Hyundai Motor <005380.KS> scale an all-time high after the car manufacturer posted record U.S. sales. The South Korea's main stock index, however, was 0.2 percent lower.

In Australia, the prospect of the central bank raising interest rates by 25 basis points to 4.5 percent at its monthly policy meeting on Tuesday cooled Monday's stock rally, sending the benchmark index <.AXJO> 0.43 percent lower around midday.

Greece's 110 billion euro ($146.5 billion) bailout, the biggest ever for a single country, eased fears of a near-term sovereign debt default, helping European shares close 0.21 percent higher on Monday <.FTEU3>

But doubts remain whether Greece will be able to carry out the tough austerity measures it promised, the package still needs parliamentary approvals and leaves open the question of whether other vulnerable European countries might also need help.

Sentiment should continue to be positive today, but markets will continue to be concerned about credit worthiness of Greece and the problem won't be resolved, said Dariusz Kowalczyk, chief investment strategist for SJS Markets.

In energy and commodities trading, the strong U.S. dollar drove safe-haven gold lower, with spot gold quoted between $1,179.40 and $1,180.20, versus Monday's notional close of $1,83.30.

Light crude for June delivery fell 0.22 percent to $86 per barrel on Tuesday, as economic optimism lifted Wall Street and on concerns that an oil spill off the U.S. Gulf Coast could disrupt short-term supply.

(Editing by Kazunori Takada)

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