The central bank is suspected to have been buying dollars in recent sessions to shore up its foreign exchange reserves, which now stand at $298.64 billion, their highest since December 2011.
On Wednesday however, views on whether or not the central bank had intervened were mixed unlike in some sessions last week, where traders suspected the central bank bought nearly $1 billion on a single day.
The rupee has remained supported by a powerful rally in Indian shares, which touched a record high for an eight consecutive session on Wednesday, on the back of strong foreign inflows.
Sentiment was also supported after the Reserve Bank of India kept interest rates on Tuesday as widely expected as it shifts to growth from boosting inflation.
"Gains in the equity markets and foreign fund inflows is helping the rupee. It may slowly go up to 59 levels by the end of this month," said Uday Bhatt, a senior foreign exchange dealer with UCO Bank.
"The central bank has been there in the market buying dollars since the rupee broke below the 61 to a dollar level. They will allow gradual appreciation in the rupee but try and curb volatility," he added.
The partially convertible rupee closed at 59.90/92 per dollar little changed compared to its Friday's close of 59.91/92. Foreign exchange markets were closed on Monday and Tuesday for a local holiday and annual closing of bank accounts.
The rupee hit 59.5950 to the dollar in intraday trade, its strongest level since July 30.
Traders will continue to monitor the domestic share market and foreign fund flows for direction.
Overseas investors have bought shares worth $64.5 million on Tuesday taking total $3.3 billion in March. Total investments in debt so far in 2014 stand at $5.8 billion.
In the offshore non-deliverable forwards, the one-month contract was at 60.32 while the three-month was at 61.01.