The rupee ended at a record closing low on November 24, weighed down by weakness in its Asian peers and dollar demand from foreign banks.
The rupee ended at 83.3675 against the US dollar, lower by 0.03% compared with its close at 83.3425 in the previous session.
The rupee hovered in a narrow range of 83.3450 to 83.38 during the day's session and fell 0.1% this week.
The dollar index last quoted steady at 103.7 but appeared on course for its second consecutive weekly loss.
Foreign banks were seen bidding for US dollars on Friday, likely on behalf of custodial clients, a foreign exchange trader at a private bank said.
The local unit has become "sticky in the 5-10 paisa zone near 83.30" the trader added.
Asian currencies edged lower as well, with the Thai baht and Korean won leading losses, falling 0.6% and 0.5%, respectively.
US Treasury yields rose in Asia with the 10-year yield climbing to 4.47% and the 2-year ticking higher to 4.94%.
Broadly, the rupee is likely to stay rangebound but small depreciations can't be ruled out, Dilip Parmar, a foreign exchange research analyst at HDFC Securities, said.
Equity inflows worth about $1.5 billion related to the rebalancing of the MSCI index, effective from Nov. 30, may offer some support to the rupee in the coming week, according to Nuvama Alternative & Quantitative Research.
Investors await the release of October inflation data in the U.S. on Thursday.
Core personal consumption expenditure inflation is expected to moderate to 0.2% month-on-month from 0.3% in September, according to a Reuters poll.
A lower-than-expected inflation print could further cement expectations that the Federal Reserve is done hiking policy rates.
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