However, a positive closing in local equities, capital inflows and a weak dollar overseas helped cap the fall to some extent, a forex dealer said.
The rupee resumed slightly lower at 60.13 a dollar from previous close of 60.12 at the Interbank Foreign Exchange (Forex) market.
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Today's closing of 60.18 is the rupee's lowest since 60.19 (July 10) versus US dollar.
The Indian benchmark S&P BSE Sensex today closed up 11.44 points, or 0.04%. FIIs injected Rs 621.68 crore yesterday, as per provisional data with stock exchanges.
The dollar index was down by 0.02% against a basket of six major currencies.
Pramit Brahmbhatt, Veracity Group CEO said: "Rupee continued to trade in a tight range to slightly weak as dollar demand from state run banks for oil importers and defence related payments balanced out the positive local equities. Expect rupee to appreciate in coming days if the local equities continues to trade higher.
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