The rupee closed at 84.0650 against the U.S. dollar, barely changed from its close of 84.0675 in the previous session.
It hit a record low of 84.0775 earlier in the session, inching past its previous all-time low of 84.0750 hit on Monday.
While Asian currencies rose on Friday, the rupee was unable to benefit from the positive cue in face of dollar bids from foreign banks and local oil companies, traders said.
Foreign investors have pulled out USD 8.4 billion so far this month from local stocks on a net basis, surpassing the previous record monthly outflow of USD 8.35 billion, recorded in March 2020.
However, foreigners' holding of Indian stocks has also ballooned over the last four years, with equities held by overseas investors having risen to more than USD 1 trillion at the end of last month.
Benchmark Indian equity indices ended the day in the green but notched their third weekly decline on the trot and are down more than 5% from their record highs hit in the last week of September.
The dollar index, meanwhile, dipped to 103.7 after hitting an 11-week high on Thursday, boosted by resilient U.S. economic data and growing odds of a Donald Trump victory in the upcoming U.S. presidential election.
"Unless markets regain some confidence in Fed cuts, the dollar will hardly face downward corrections in the near term," ING Bank said in a note.
Interest rate futures are currently pricing in 44 basis points worth of rate cuts across the Federal Reserve's two remaining policy meetings in 2024.
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