The rupee is likely to be supported by strong foreign inflows that helped push up the BSE Sensex and NSE Nifty indexes to record highs on Tuesday, but traders expect more narrow ranges given the lack of specific domestic triggers.
Global factors will also be key this week, ahead of the Federal Reserve's two-day meeting ending on Wednesday, continued political tensions in Ukraine, and a weakening yuan currency in China.
"There aren't any domestic data points so rupee should broadly hold in a 60.60 to 61.75 range with good demand from oil firms being seen," said Hari Chandramgethen, head of foreign exchange trading at South Indian Bank.
"A breach of 60.60 on the downside for the pair can take it to 60.10 levels," he added.
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The partially convertible rupee closed at 61.19/20 per dollar, unchanged from Friday. Financial markets were closed on Monday for a local holiday.
The rupee earlier rose to as high as 60.88 per dollar in early trade, its highest since March 11, as foreign investors continued to bolster blue chips in the lead-up to general elections.
Overseas funds were net buyers of $160.6 million worth of shares on Friday, marking their 20th net buying session in the previous 21, for a net total of $1.6 billion, exchange and regulatory data shows.
In the offshore non-deliverable forwards, the one-month contract was at 61.67 while the three-month was at 62.42.
* Rupee ends unchanged at Friday's close of 61.19/20
* Demand from oil firms, profit-taking in shares hurts
* Rupee seen in 60.60 to 61.75 range in the near term