However, for the week, the rupee fell 0.5 percent against the dollar, posting its worst performance since the week ended Jan. 24, with trading influenced by falls in regional currencies on a weekly basis amid worries over tensions in Ukraine and a slide in the Chinese yuan.
The rupee has fallen for four consecutive weeks, retreating ever since it hit an eight-month high of 59.5950 in early April.
Although continued strong foreign purchases of Indian shares have helped support the rupee, any changes in those flows could impact the local currency, with investors still focused on the outcome of the national elections due in mid-May.
"There was good dollar selling by foreign banks and a couple of corporates. Good position cutting (long dollar) was seen once the rupee broke below 60.80 levels," said Hari Chandramgethen, head of foreign exchange trading at South Indian Bank.
"We could see the rupee hold in a 60.20 to 61.20 range next week," he added.
The partially convertible rupee closed at 60.60/61 per dollar compared with 61.07/08 on Wednesday, rising 0.8 percent on day, its biggest single-day gain since March 6.
Financial markets in Mumbai were closed on Thursday on account of polling for the national elections in the state.
Trading was dominated by dollar sales from custodian banks, offsetting the strong month-end demand from importers.
That dollar demand helped offset a fall in domestic shares, which retreated from their fourth consecutive record highs hit earlier in the session on disappointment over earnings.
The rupee did not see any major impact from the below-average monsoon rainfall prediction by the meteorological department which could stoke inflation and hit the economy as investors remained focussed on the ongoing national polls.
In the offshore non-deliverable forwards, the one-month contract was at 61.05 while the three-month was at 61.88.
Remittances rise as NRIs bet on strong rupee
Economy ready to take off, says minister
Rupee falls for second day; weak Asian peers hurt
Sensex drops 188 points amid growth concerns
Rupee hits 8-month closing high; state-run banks buy dollars