MUMBAI (Reuters) - The Indian rupee closed slightly down on Monday, unable to build on recent gains as local dollar demand pressured the currency even as most of its Asian peers rose.

The rupee ended at 83.13 against the U.S. dollar, against its close at 83.0975 in the previous session. The rupee had rallied to a two-month high of 83.0250 on Friday.

The dollar index declined 0.1% to 104.6 extending its decline from Friday, while most Asian currencies rose between 0.1% to 0.4%.

Trading volumes were relatively muted with the U.S. holiday "keeping the market steady", a foreign exchange trader at a private bank said.

U.S. and U.K. markets were shut on Monday.

Meanwhile, benchmark Indian equity indices BSE Sensex and Nifty 50 hit record highs but ended the session in the red.

Foreign flows into Indian equities are likely to be a key driver for the rupee this week as investors position for the outcome of the country's national elections on June 4.

Overseas investors have net sold $2.6 billion of Indian stocks so far in May, according to depository data.

"Looking at Asian currencies and economic data out of U.S., USD/INR may again bounce back to 83.30-40 levels with RBI (Reserve Bank of India) also likely to intervene (to buy the pair) at lower levels," Abhilash Koikarra, head of forex and rates at Nuvama Professional Clients Group said.

Meanwhile, dollar-rupee forward premiums declined with the 1-year implied yield down 2 basis points at 1.64% after investors pared expectations of rate cuts by the Federal Reserve.

Investors are currently pricing in 34 basis points of rate cut over 2024, down from near 50 basis points of cuts expected earlier this month.

(Reporting by Jaspreet Kalra; Editing by Mrigank Dhaniwala)

By Jaspreet Kalra