The rupee closed at 83.4875 against the U.S. dollar, weaker than its previous close at 83.4225.
Most Asian currencies rose with the Korean won up 0.9% and leading gains, while the offshore Chinese yuan was down 0.2%. Weakness in the offshore yuan also weighed on the rupee.
The dollar index was steady at 105.1 after dipping to a near one-month low on Friday after U.S. economic data raised investor expectations that the Federal Reserve may cut policy rates twice this year.
Dollar demand from importers, including local oil companies, pushed the rupee lower on Monday, a foreign exchange trader at a state-run bank said.
Meanwhile, dollar-rupee forward premiums inched up with the 1-year implied yield up 2 basis points (bps) at 1.68%, aided by a dip in near-maturity U.S. bond yields.
The one-year Treasury yield edged lower in Asia to 5.12% after falling about 4 bps on Friday. The 10-year U.S. Treasury yield dropped to the lowest in three weeks on Friday after data showed that the world's largest economy added fewer jobs than expected.
The US unemployment rate ticked higher, while wages grew less than forecast.
In the near term, the rupee is expected to maintain a "mild depreciation bias", till it holds below 83.30, Dilip Parmar, a foreign exchange research analyst at HDFC Securities said.
Investors now await remarks from Fed policymakers due later in the day for cues on policymakers' thinking about the future path of policy rates.
In recent speeches, Fed officials have emphasised that they expect inflation to decline with the central bank holding rates steady.
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