MUMBAI - The Indian rupee closed little changed on Monday as dollar demand from state-run banks offset positive cues from an uptick in most Asian currencies.

The rupee ended at 82.89 against the U.S. dollar, barely changed from its previous close of 82.90. The currency moved in a tight band between 82.86 and 82.9125 through the day's session.

The dollar index was largely steady near 103.8 on Monday, while most Asian currencies rose, with the Malaysian ringgit up nearly 0.5% and leading gains.

While the rupee opened stronger at 82.86, dollar demand from state-run banks eroded gains, a foreign exchange trader at a foreign bank said.

Since early in the session, state-run banks were seen bidding for dollars, making it hard for the rupee to hold onto its opening uptick, traders said.

Asian currencies were lifted by a dip in U.S. bond yields after data on Friday indicated that U.S. manufacturing activity contracted more than expected in February.

While the rupee's intraday moves have "mostly been sideways," in recent sessions, the domestic unit is likely to keep appreciating in a "slow and steady," manner, Dilip Parmar, a foreign exchange research analyst at HDFC Securities, said.

The focus this week will be Federal Reserve Chair Jerome Powell's testimony to U.S. lawmakers on Wednesday and Thursday, which may offer cues on the central bank's thinking about the future trajectory of policy rates.

U.S. jobs data for February is due on Friday and will also be closely watched by investors after January's blowout jobs report prompted a pullback in bets of sharp Fed rate cut bets.

Investors are currently pricing in a nearly 72% chance of a rate cut in June, up from about 61% a week earlier, according to the CME's FedWatch tool.

(Reporting by Jaspreet Kalra; Editing by Sonia Cheema)