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.
The rupee had gained 6 paise to close at 60.07 against the dollar in Thursday's trade on fresh selling of the American currency by banks and exporters in view of strong capital inflows.
The rupee closed 2 paise lower at 60.13 on Wednesday as a sudden demand for the US currency emerged at fag-end of trade.
The rupee had gained 10 paise to close at 60.11 against the dollar in Tuesday's trade on fag-end selling of the US currency by banks and exporters.
In New York market, the dollar was little changed against major rivals yesterday as investors continued to comb through economic data and speeches from central bank officials to get a better sense of when the Federal Reserve could begin to raise interest rates.
The rupee had lost 31 paise to close at one-month low of 61.07 on Wednesday on sustained dollar demand from banks and importers.
The rupee closed at 60.76/77 on Tuesday.
Dealers attributed the fall in the rupee on Tuesday to dollar's gains against other currencies overseas, but a higher opening in the domestic equity market capped the fall.
Forex dealers said strengthening of dollar against other currencies in the global market also put pressure on the rupee but a higher opening of the domestic equity market limited the fall.
Foreign funds sold Indian shares worth 446.9 million rupees ($7.4 million) on Wednesday, provisional exchange data showed, marking the third consecutive session of outflows.
In New York Market, the US dollar rose against the Australian dollar on Tuesday as gold futures dropped more than two per cent and investors anticipated Chinese data that is likely to show a slowing of growth.
The rupee had lost 26 paise to close at 60.16 against the dollar yesterday on fresh dollar demand from banks and importers in view of the US currency gaining overseas and weakness in local equities.
The rupee closed at 59.90 in Wednesday's trade, gaining just one paisa from its previous close.
The rupee had gained 40 paise to close at an eight-month high of 59.91 against the dollar on Friday.
The rupee closed at 60.31/32 on Thursday.
In the global markets, the euro was under pressure against the US dollar yesterday, dragged lower as European monetary policy officials indicated willingness towards supporting more stimulus measures to aid the regional economy.
In New York market, the US dollar cut its rise after a round of mixed US data yesterday, but held narrowly higher against key rivals.
Domestic shares jumped nearly 1.5 per cent on Monday to an all-time high, surpassing their previous record hit just last week, as lenders including ICICI Bank extended a recent rally.
The rupee had depreciated by 39 paise, logging its biggest daily loss in nearly two months, to end at 61.34 on Thursday on fears of capital outflows from emerging markets after Federal Reserve signalled a sooner-than-expected hike in US benchmark interest rates.