The US dollar ended sharply dearer against the rupee at 63.53/54 per dollar.
The pound sterling also finished higher at Rs 99.84/86 per pound at the Interbank Foreign Exchange market.
Commerce Secretary Rajiv Kher said the government would get uncomfortable if the Indian currency stays in this range for long.
"The exchange price has come down to 63. As the Secretary of the Department of Commerce I feel that the rupee if it goes further down, or stays for too long at this point, it should give me a reason to feel a little concerned," Kher told reporters at the India Engineering Sourcing Show (IESS).
When asked whether the issue has been discussed with Finance Ministry or the RBI, Kher said: "Every time I meet Finance Secretary, I am not talking about weather".
Kher described the range between 60 to 62 as a "good level", adding that the government will become "uncomfortable" if it crosses that band.
This was due to heavy dollar demand from importers amid falling crude oil prices.
Forex dealers said besides continued demand for the American currency from importers, increased capital outflows by foreign funds also kept pressure on the rupee.
The three-day IESS provides a platform for 310 international and Indian engineering firms, including big players like BHEL, Bajaj Steel Industries, Finolex Cable, HECL, Kirloskar Brothers, Atul Auto, Mazagon Dock, MMTC and SIDBI, organisers of the event, EEPC India, said.
Global giants like automobile major Fiat from Italy, Home Depot from the US and Spanish firm SECO are aiming to explore sourcing avenues for their businesses in India, they said.
($1 = 62.9050 rupees)