Renewed protests in Hong Kong added to the nervous mood.
“For the day, we expect volatility for the rupee to be confined to a narrow range of 75.40 and 76.20,” MOSL said.
Strengthening of the American currency overseas also weighed on the domestic unit.
In Asian trade, the dollar edged higher on Wednesday as worries about the US response to China's proposed security law for Hong Kong supported safe-haven demand for the greenback, Reuters reported.
The dollar edged up to $1.2321 against the pound on Wednesday in Asia, pulling away from its lowest level in two weeks.
On Friday, rupee had settled at 75.95 against the US dollar.
The trade-sensitive Australian and New Zealand dollars each rose about 0.7 per cent.
“For the day, we expect the rupee (Spot) to quote in the range of 75.40 and 76.20,” MOSL said.
In onshore trade, the yuan eased slightly to 7.1422 per dollar, approaching the lowest in more than seven months.
During the trading session, it touched an intra-day high of 75.71 and a low of 75.95.
Das said inflation outlook is highly uncertain and India is seeing a collapse in demand.
On Wednesday, the rupee had settled at 75.80 against the US dollar.
Motilal Oswal Financial Services believes the local unit will remain under pressure on the back of fund outflows by the FIIs from the equity and debt segment.
"I think they might keep going," said Westpac FX analyst Imre Speizer.
On Tuesday, the rupee had settled at 75.66 against the US dollar.
On the domestic front, market participants will be keeping an eye on the growth number that will be released later next week.
The dollar also edged higher against the safe-haven yen to edge near a five-week high though it was capped by renewed scepticism on coronavirus vaccine developments.
On Monday, the rupee had settled at 75.91 against the US dollar.
“Rupee is expected quote in the range of 75.20 and 76.20,” brokerage Motilal Oswal Financial Services said in a report.
The euro held onto hefty gains against the Swiss franc and the dollar following a proposal by France and Germany for a 500 billion euro ($543 billion) recovery fund offering grants to regions hit hardest by the coronavirus crisis.
The local unit opened sharply lower at 75.85, then lost further ground to finally settle at 75.91 against the US dollar, down 33 paise over its previous close.
In the last few sessions, rupee has been consolidating in the range of 75 and 76 (Spot).
In the previous week, the reserves had increased by $1.622 billion to $481.078 billion.
On Thursday, the rupee had settled 10 paise lower at 75.56 against the US dollar.
The local currency traded in a narrow range on Thursday despite sharp losses in domestic equities.
Against a basket of currencies the dollar is up about 0.5% this week.
It had settled at 75.46 against the US dollar on Wednesday.
According to CLSA, measures announced by the government so far are not enough to satisfy elevated expectations.
The dollar traded at $1.0818 against the euro on Thursday following a 0.3% gain in the previous session.
On Tuesday, the rupee had settled at 75.51 against the US dollar.
The local currency on Tuesday advanced over 20 paise ahead of inflation and industrial production number that was released after market close.
The euro changed hands at $1.0848 after having gained about 0.4% in the previous session.
Currency traders expect the rupee to trade in the band of 74.5-76.
During the day, the domestic unit hit an intra-day high of 75.49 and a low of 75.95 against the greenback.
The local currency on Monday depreciated by 19 paise to close at a one-week low of 75.73 against the greenback due to fiscal deficit concerns.
The biggest loser was the Australian dollar, which dropped about 0.8% to a one-week low, while the kiwi extended falls.
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