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Traders work on the floor of the New York Stock Exchange January 15, 2016.Reuters file

Asian shares fell on Tuesday, tracking weak U.S. stock futures while dollar steadied after bouncing from three-year lows.

Traders took their cue from European markets, which fell 0.6 percent on Monday following three days of large gains. U.S. stocks took a break for Presidents' Day holiday while Chinese mainland markets open to trading on Thursday.

MSCI's broadest index of Asia-Pacific shares outside Japan edged down 0.1 percent. Japan's Nikkei shed 0.4 percent after three successive days of gains.

Back home, SGX Nifty, an early indicator of the Nifty 50's trend in India, signals a weak start for the domestic markets after the benchmark Sensex declined 236 points or 0.69 percent to close at 33,774 on Monday.

The partially convertible rupee ended at 64.22 per dollar on Friday from its previous close of 63.91 per dollar. India currency and debt markets were closed on Monday for a public holiday.

So far this year, the rupee has fallen 0.54 percent against the U.S. dollar, while overseas investors have bought $1 billion from local equity and $1.9 billion in debt markets.

F&O Expiry: Trading is likely to be volatile this week as traders will roll over positions in the futures and options segment from the February 2018 series to March 2018 series.

Crude check: Brent crude declined 0.38 percent after two-day gains at $65.42 per barrel while the West Texas Intermediate crude climbed 1.1 percent to $62.37 a barrel.

Fed minutes: On Wednesday, the U.S. Federal Reserve will release the minutes from its January meeting at which the central bank opted to leave interest rates unchanged but upgraded its inflation outlook.

Fed speeches: A slew of Fed policy makers are due to speak this week including New York Fed President William Dudley and Atlanta Fed President Raphael Bostic.