Besides, steady euro against the American unit and a higher opening in the domestic equity market supported the rupee, forex dealers said.
Foreign institutional investors pumped around Rs 100 crore (Rs 1 billion) in stocks on Tuesday.
Some weakness in the local stock market amid a rising trend pared rupee's early gains, forex dealers said.
Continued dollar selling by exporters and some banks on hopes of further fall in dollar value overseas also aided the rupee rise.
Banks and exporters preferred to reduce their dollar position on hopes of further capital inflows as foreign portfolio investors infused $107.22 million yesterday as per the record of Securities and Exchange Board of India.
The rupee rose by 7 paise to Rs 55.68 against the US dollar in early trade today on the Interbank Foreign Exchange as the American currency weakened against euro overseas.
The rupee fell by 34 paise to 55.99 against the US dollar in early trade at the Interbank Foreign Exchange market today as the American currency gained against other currencies overseas.
Banks and exporters preferred to reduce their dollar position at the current stage in view of sustained capital inflows coupled with weakness in dollar overseas, forex dealers said.
A weak dollar in overseas market in view of the Federal Reserve's cautious stance on interest rate strengthened the rupee value.
The rupee hovered in a range of 63.75 and 63.84.
Forex dealers said dollar selling by exporters and a higher opening in the equity market also supported the rupee.
The rupee resumed better at 54.52 a dollar from previous close of 54.56 at the Interbank Foreign Exchange market and immediately touched a low of 54.56.
The dollar index was trading lower by 0.03 per cent against its major global rivals today.
Investors are anxious over the US-China trade tension, a sharp devaluation in yuan and uncertainty over Kashmir issue.
The rupee had gained 16 paise to close at over one-month high of 62.16 on Monday against the American currency on persistent selling of dollars by banks and exporters on hopes of capital inflows into domestic markets.
The rupee on Thursday lost 25 paise to 55.72 against the US dollar in early trade at the InterbankForeign Exchange market as the American currency gained strength against other currencies overseas.
Snapping its two-day losing streak, the rupee on Monday bounced back by 9 paise to 66.67 against the US dollar.
The local currency commenced lower at 54.03 a dollar on Monday's close of 53.86 at the Interbank Foreign Exchange market.
Therupee staged a smart rebound from its low towards the fag-end trade on dollar selling as well as suspected intrusion by the Reserve Bank to end steady at 63.39.
In the last four days, rupee has lost 104 paise against the dollar.
The domestic currency has fallen past the 56-level against the dollar after June 29.
Dealers said apart from gains in euro and the Asian currencies against the American currency overseas, higher opening in the domestic equity market and selling of dollars by exporters and some banks supported the rupee.
On Wednesday, the rupee ended barely steady at 64.93.
In New York, the dollar index climbed to its highest level in about two years on Wednesday.
Weak trends in local stocks with Sensex dropping by 129 points also weighed on rupee but some capital inflows limited its decline to some extent, forex dealers said.
On Monday, the biggest gainers in the Sensex pack were Sun Pharma, Bajaj Finance, Vedanta, Yes Bank, Tata Motors, HCL Tech, IndusInd Bank and Kotak Bank, HCL Tech, Infosys and Bajaj Auto.
The Indian rupee continued to rule firm in the late morning session by improving five paise to 53.11 per dollar on selling of dollars by banks in view of persistent foreign capital inflows.
The dollar strengthened against other currencies as well in the overseas market.
Penalty must act as a deterrent. If it is too low, it could encourage the regulated entities to lap up penalty instead of complying with the norms, suggests Tamal Bandyopadhyay.
The rupee resumed higher at the Interbank Foreign Exchange market but fell to a intra-day low of 57.10.
The currency hit a record low of 57.32 on June 22 and has so far shed 7 per cent value against the dollar in 2012, making it worst performing currency in Asia.
The rupee on Tuesday rose by 11 paise to 56.90 against the US dollar in early trade at the Interbank Foreign Exchange market as the American currency weakened against euro and other currencies overseas.
On Tuesday, the rupee had closed three paise down at 55.96 against the dollar amid foreign fund outflows and demand of the US currency from importers.
The rupee on Tuesday again breached the 56-level by falling 12 paise to 56.05 against the US dollar in early trade on the Interbank Foreign Exchange on increased demand for the American currency from banks and importers.
The rupee on Tuesday tumbled by 32 paise to close at 64.17 on fresh dollar demand from importers.
The rupee commenced higher at 55.14 a dollar from the overnight close of 55.36 at the Interbank Foreign Exchange market, and immediately touched a low of 55.30 on some dollar demand from oil importers as crude oil hovered around the $85 per barrel.
The partially convertible rupee was trading at 65.87/88 per dollar.
The rupee had lost 11 paise to close at 55.65 against the Greenback on Monday due to late dollar demand from importers.
Forex dealers said besides dollar's gains in the overseas markets, a weak opening in the stock market following capital ouflows, also put pressure on the local unit.
Dealers said Euro's gains against the dollar in overseas markets and step taken by the RBI to stablise the rupee mainly influenced the trading sentiment.
