MUMBAI, April 25 (Reuters) - The Indian rupee eased slightly against the greenback on Tuesday, tracking the weakness in its Asian peers, with likely importer-led dollar demand also weighing on the local currency.

The rupee traded at 81.9475 to the U.S. dollar by 10:30 a.m. IST compared with 81.9050 in the previous session.

The rupee on Monday had managed to strengthen past 82 on dollar sales by foreign banks, likely related to their custodial clients.

A move below that level is "sure" to attract importers and bids from public sector banks, so the rupee will find it difficult to move past the 81.90-to-81.95 levels, traders said.

"The rupee is expected to trade between 81.75 to 82.10 levels during the day. Importers are advised to increase their hedges at the current level near 81.90," said Ritesh Bhansali, vice president at Mecklai Financial Services.

The offshore Chinese yuan and the South Korean won fell more than 0.20% on the day, while Asian equity gauges also declined as risk sentiment remained frail in the week before the Federal Reserve's meeting.

The dollar index struggled to make meaningful gains on fresh worries about the health of domestic lenders and the rally in the euro.

The plunge in First Republic Bank's deposits, reported overnight, served as a reminder that risks to stability have not entirely died down and prompted traders to renew expectations that the Fed will shift quickly from hiking to cutting rates.

Meanwhile, the euro rose above $1.10 overnight on firming bets of the European Central Bank (ECB) raising rates.

ECB board member Isabel Schnabel told Politico that a 50 basis points hike was not off the table and would depend on data - notably inflation figures due two days before May's meeting. (Reporting by Anushka Trivedi; Editing by Savio D'Souza)