The rupee closed at 86.5675 against the U.S. dollar, up from its close at 86.61 in the previous session.
The dollar index was down 0.2% at 109.1 while Asian currencies were mostly higher between 0.1% and 0.7%.
The offshore yuan rose to a two-week high buoyed by a friendly call between Trump and Chinese President Xi Jinping on Friday and better-than-expected fourth-quarter Chinese economic data.
With Trump set to return to the White House, financial markets are expected to take their cues from policy announcements coming out of Washington this week. U.S. markets are closed on Monday for the Martin Luther King Jr. Day holiday.
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