The rupee pulled back from the day's low on Monday buoyed by dollar sales from some local companies, although weakness in local equities on signs of cooling domestic growth weighed.
However, strong demand for dollars due to worries North Korean leader Kim Jong-il's death could spark political instability in the region kept the local currency on the edge, traders said.
Fears of sovereign downgrades over the euro zone debt crisis pressured the euro on Monday, while news of the death of North Korean leader Kim Jong-il fed fears of regional instability in Asia.
The rupee closed at 52.88/90 to the dollar, 0.3 percent weaker from its 52.70/72 close on Friday, after moving in a wide 52.72-53.25 band during the day.
There is some calm returning to the market post the Reserve Bank of India's steps on trading limits last week, said Uday Bhatt, senior manager of dealing at UCO Bank.
People now can't afford to keep positions open for long and there was also a bit of dollar selling by some corporates. Overall, the rupee should move in 52-53 band this week.
Last Thursday, the RBI reduced net overnight open position limit or trading limit of banks to cut speculation from the domestic currency market which saw the rupee hit a record low of 54.30 against the dollar.
Traders said that although the RBI's move could have lowered speculation, the turnover in the dollar-rupee market had dropped sharply since then and lowered the price-making ability of banks for customers.
The market has kind of dried up post the RBI's measures and the quotes too seem wider, said a dealer with a foreign bank.
However, most dealers agree that as a result of the recent measures, the RBI was now in a better position to stabilise any sharp volatility in the local currency.
The currency had rebounded last week after hitting a record low of 54.30 on Thursday on suspected central bank intervention.
The RBI's policy on the currency has been to intervene only to smoothen volatility and not target a level.
The relatively small size of its kitty of foreign currency reserves, compared with some other Asian economies, and a widening trade deficit means the RBI needs to calibrate moves in the foreign exchange market carefully.
The BSE Sensex fell 0.72 percent on Monday to their lowest close since August 2009, as investors continued last week's selloff on mounting concerns over slowing growth in Asia's third-largest economy amid lingering global economic uncertainty.
The offshore non-deliverable forwards (NDFs) were indicating further weakness, with the one-month rupee NDFs at around 53.24.
The one-month onshore forward dollar premium was at 37.5 points, up from 32.5 on Friday and the three-month premium was at 98 points, up from 89. The one-year premium was at 267.25 points, higher from 245.75 points.
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 ended at 53.0600, 53.0650 and 53.0475 respectively. Total volume was at $4.99 billion.