Traders expect the rupee to remain wedged between the 59.60 and 60.50 levels in the absence of any key triggers in the near-term.
Traders also say oil-related dollar demand is capping broader gains in the rupee.
The partially convertible rupee closed at 60.30/31 per dollar compared with 60.28/29 on Friday.
The partially convertible rupee closed at 60.19/20 per dollar versus its close of 59.75/76 on Wednesday after earlier gaining to a one-week high of 59.57.
Forex dealers said though increased demand for the US currency from importers put pressure on the rupee but a higher opening in the domestic equity market and the dollar's rise against other currencies overseas, capped the losses.
It moved in a range of 59.80 and 59.99 per dollar during the morning deals.
The rupee resumed higher at 59.69 per dollar as against the last closing level of 59.73 at the Interbank Foreign Exchange market.
The Bombay Stock Exchange has resumed trading after three hours on Thursday.
n New York market, the dollar posted second-quarter losses against nearly all major rivals yesterday, with the exception of the euro.
The rupee resumed higher at 60.13 per dollar as against the last closing level of 60.20 at the Interbank Foreign Exchange market, and hovered in a range of 60.07 and 60.18 per dollar before quoting at 60.08 at 1000 hours.
These sectors have underperformed the wider market over the past year and are seen having far more upside potential if the economy picks up thanks to Modi's reformist agenda.
Forex dealers said besides increased dollar selling by exporters, strength in other currencies against the American currency overseas also supported the rupee but a lower opening of the domestic equity market capped the gains.
Traders will continue to focus on the measures new Prime Minister Narendra Modi-led government will take to bring down the fiscal deficit and fight inflation.
The investment bank also says no ministries were merged even as some ministers were given more than one portfolio.
Central bank steps up dollar purchases to check rupee gains
The benchmark has gained 2 per cent this week on continued hopes the incoming Narendra Modi government would unveil substantial economic reforms.
The moves by the RBI, announced late on Wednesday, should increase supplies of gold and brighten the earnings outlook for jewellery makers after the government took tough measures to curb imports last year, analysts said.
The rupee had surged 37 paise to end at a nine-month high of 59.68 against the dollar on Tuesday. Forex market remained closed on Wednesday for 'Buddha Purnima'.
Weakness of the dollar in the overseas market also boosted the rupee, a forex dealer said.
Most dealers said the heavy buying by state-run banks was on behalf of the central bank, looking to limit the volatility in the rupee, in the face of foreign fund flows into the share market.