By Lisa Twaronite

TOKYO (Reuters) – Asian shares fell in early trading on Tuesday, while the dollar held near highs scaled in holiday-thinned trading in the previous session.

European shares marked a weak finish in thin trade on Monday, with many markets in the region closed for holidays. U.S. markets were also closed for Memorial Day.

MSCI’s broadest index of Asia-Pacific shares outside Japan was down 0.2 percent in early trade, after eking out a late gain in the previous session.

Japan’s Nikkei stock index (.N225) edged up 0.1 percent, after logging seven straight gains and closing at a fresh 15-year high on Monday.

The dollar hit a one-month high against a basket of major currencies on Monday in the wake of Friday’s comments from Federal Reserve Chair Janet Yellen, who rekindled market expectations that the central bank was gearing up to hike interest rates.

The dollar index (.DXY) rose as high as 96.475 on Monday, after Yellen said she expected economic data to strengthen and noted that some of the U.S. economy’s weakness at the start of the year might be due to “statistical noise.”

But Fed Vice Chair Stanley Fischer said in Israel on Monday that too much importance was being placed on the central bank’s first rate hike, and that the process of returning to more normal levels of interest rates will take a few years.

While markets largely expect the first rate hike in September, it will be determined by data and not by date, he said.

Investors await the latest batch of U.S. data later on Tuesday that could provide more clues on the strength of economic recovery, including May durable goods and April consumer confidence. (ECONUS)

Greece’s ongoing debt crisis kept pressure on the euro. Time is running out for Greece to reach an agreement on reform with lenders and there will be no further funds for Athens without it, the head of the European Stability Mechanism, Klaus Regling, told Germany’s Bild newspaper on Tuesday.

“The Greek political saga will remain in the spotlight as the deadline for payments to the IMF approaches”, strategists at Barclays wrote in a note to clients. “A light data calendar and continued political uncertainty in Greece should continue to weigh on EUR,” they said.

The euro was down about 0.1 percent at $1.0969 (EUR=), not far from its overnight low of $1.0959 and wallowing at its lowest levels since late April.

The dollar was slightly higher against the Japanese currency at 121.60 yen (JPY=) after rising as high as 121.78 yen on Monday, its highest since March 10.

Crude oil edged up, after marking gains in Monday’s thinned trading as firm global demand offset the effects of a stronger dollar.

Brent crude (LCOc1) rose about 0.1 percent to $65.57 a barrel, while U.S. crude (CLc1) added 0.2 percent to $59.86.