The rupee was at 83.1750 against the U.S. dollar as of 09:45 a.m. IST, its highest since April 10, and up 0.1% from its close at 83.28 on Wednesday.
Indian debt and FX markets were shut on Thursday for a local holiday.
Dollar sales from foreign banks, likely on behalf of custodian clients, aided the rupee, a foreign exchange trader at a state-run bank said.
Foreign investors net bought USD 560 million of Indian stocks on Thursday, according to provisional data from the National Stock Exchange of India.
Benchmark equity indices, BSE Sensex and Nifty 50 , climbed to all-time highs on Friday.
The dollar index rose above 105 and Treasury yields ticked up in light of robust U.S. economic data, which prompted investors to pare expectations of the Federal Reserve easing interest rates this year.
U.S. initial jobless claims dropped more-than-expected and business activity accelerated to the highest in more than two years in May, data released on Thursday showed.
Odds of rate cut in September have declined to about 53%, down from 57% a day earlier, according to CME's FedWatch tool.
Meanwhile, dollar-rupee forward premiums slipped, with the 1-year implied yield down 3 basis points (bps) at 1.66%, pushed lower by the uptick in U.S. bond yields.
The 1-year U.S. Treasury yield rose 4 bps on Thursday and extended its rise to 5.22% in Asia hours.
The "overall outlook for rupee appears strongly positive", Amit Pabari, managing director at FX advisory firm CR Forex, said.
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