The forex market was closed on Wednesday, February 19, in view of "Chatrapati Shivaji Maharaj Jayanti".
However, recovery in local equities and sustained capital inflows capped the rupee fall, a forex dealer said.
The US manufacturing activity, which hit its highest in nearly four years, supported the dollar, ultimately weighing on the rupee.
At the Interbank Foreign Exchange (Forex) market, the domestic unit commenced slightly lower at 61.96 a dollar from last weekend's close of 61.93 and moved in a wide range of 61.83 and 62.45 before settling at 62.12, revealing a fall of 0.19 paise or 0.31 pct.
In last two weeks, it had risen by 75 paise or 1.20 pct.
The benchmark S&P BSE Sensex made a strong rebound and closed up by almost 334 points or 1.64 pct while FIIs infused USD 232.45 million during the week till February 20.
Pramit Brahmbhatt, CEO, Alpari Financial Services (India), said, "After gaining for two consecutive weeks, the rupee closed on a weak note taking cues from strong dollar index as yesterday US dollar jumped against the Australian dollar after a weaker-than-expected reading of a Chinese manufacturing estimates were released."
"The dollar demand from local oil importers further dented the rupee movement. Expect rupee to depreciate further in coming days as despite of mixed data released yesterday which has raised the concerns about the economic growth, Investors have chosen dollar over the safe havens which will force rupee to trade weak. The trading range for the USD/INR pair is expected to be within 61.50 to 63.00.