The main stock index dropped 0.4 percent, taking cues from mostly lower Asian markets and after three bombs rocked crowded districts of Mumbai late on Wednesday, killing at least 17 people.
Traders said the lack of any large swings in the stock market after the bomb blasts kept the sentiment in the forex market unaffected.
At 10:45 a.m. (0516 GMT), the partially convertible rupee was at 44.49/50, stronger than its last close of 44.52/53, but down from a high of 44.4425 touched in early trades.
The unit has so far moved in a range of 44.4425-44.5200 and is expected to stay in a 44.42-44.55 band during the day.
"Euro is being supportive, but local shares are pulling rupee down," said a foreign exchange dealer with a private-sector bank.
The euro was $1.4211 and the index of the dollar against six major currencies was down 0.41 percent at 74.898 points.
The euro had been $1.4081 at the end of domestic currency market on Wednesday and the index was at 75.606 points.
The US dollar was on the run in Asia on Thursday after a ratings warning from Moody's and a hint of further policy easing from the Federal Reserve unleashed a wave of panic selling, much to the relief of the hard-pressed euro.
Most Asian units too were stronger against the US unit.
Traders would also be watching monthly inflation data due at 0630 GMT for its impact on the stock market. India's wholesale price index probably rose 9.70 percent in June from a year earlier, quickening from May, on rising food and fuel prices, a Reuters poll showed.
The one-month onshore forward premium was at 23.75 points from 23.50 on Wednesday, while the three-month was at 69.50 points from 70.75 and the one-year was at 232 points versus 235.25.
One-month offshore non-deliverable forward contracts were quoted at 44.66, weaker than the onshore spot rate.
In the currency futures market, the most traded near-month dollar-rupee contracts on the National Stock Exchange, the MCX-SX and the United Stock Exchange were all at 44.6000. The total volume was at $2.42 billion.
Copyright Reuters, 2011