The rupee closed at 83.4925 against the U.S. dollar, barely changed from its close of 83.4850 in the previous session. The currency hovered between 83.44 and 83.50 throughout the session.
Both dollar bids and offers from state-run banks contributed to keeping the rupee in a tight band, traders said.
"Bids from state-run banks capped the rupee's gains around 83.44 and they were also on offer near 83.48 in the second half (of the session)," a foreign exchange trader at a foreign bank said.
The dollar index was at 104.9 while Asian currencies were mixed after modestly rising against the U.S. dollar earlier in the session.
"Buying on dips between 83.20-83.10 and selling on upticks between 83.50-83.70 is suggested (on the dollar-rupee pair)," Amit Pabari, managing director at FX advisory firm CR Forex said.
Meanwhile, dollar-rupee forward premiums ticked up, with the 1-year implied yield touching a one-month peak of 1.66% aided by a decline in U.S. bond yields.
The 1-year U.S. Treasury yield fell to 5% on Friday, its lowest since April, before nudging up in Asia trading.
Odds of a September rate cut by the Fed have risen to nearly three-in-four, after data on Friday signalled cooling in the U.S. labour market, weighing on the dollar and U.S. bond yields.
Federal Reserve Chair Jerome Powell's semi-annual monetary policy testimony to U.S. lawmakers will be in focus on Tuesday and Wednesday for additional cues on the future path of U.S. policy rates.
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