The local currency weakened despite FII inflows worth nearly $70 million (R374 crore) in stocks.
The local currency opened lower at 54.10 per dollar as against the last weekend's level of 53.81 at the Interbank Foreign Exchange (Forex) Market.
For some time rupee hovered in a narrow range, before dropping to 54.65 after importers and banks rushed to buy dollars.
In Tokyo, the dollar hit a two-month high against a basket of major currencies on Monday after the job reports last week highlighted relatively solid US economic fundamentals.
At closing, the rupee finished a tad better from day's lowest levels closing at 54.61 per dollar, a loss of eightypaise or 1.49% from previous closing.
The rupee had last ended at 55.43 per dollar on September 13, 2012.