MUMBAI - The Indian rupee gained on Tuesday, boosted by dollar sales from state-run banks, likely on behalf of merchant clients, but traders expect the domestic currency's gains to be limited as importers may step in to cover hedging requirements.

The rupee was at 83.4750 against the U.S. dollar as of 10:00 a.m. IST, up 0.08% from its close of 83.5550 on Friday.

Indian financial markets were shut on Monday for a holiday.

"We expected to see bids after the lower opening (on USD/INR) but state-run banks are on offer," a foreign exchange trader at a foreign bank said, adding that the dollar offers were most likely related to client orders.

The rupee is likely to remain rangebound between 83.40 and 83.70 this week, Dilip Parmar, a foreign exchange research analyst at HDFC Securities, said.

"Expecting minor depreciation before strength in the rupee," he added.

Meanwhile, the dollar index was up 0.1% at 105.4 during Asian hours, with Asian currencies mostly rangebound ahead of U.S. retail sales data later in the day. The report could influence expectations of when the Federal Reserve may begin easing policy rates.

"I think one rate cut would be appropriate by year's end," Philadelphia Fed President Patrick Harker said on Monday, referring to his base case of slowing but above-trend economic growth, a modest rise in unemployment, and a "long glide" back to target for U.S. inflation.

While data has hinted that U.S. inflation may be cooling, Fed officials have maintained a cautious stance on the future trajectory of interest rates.

Investors will also keep a tab on remarks from a slew of Fed policymakers later in the day.

(Reporting by Jaspreet Kalra; Editing by Sonia Cheema)