The domestic unit resumed lower at 68.60 per dollar as against last Thursday's closing level of 68.46 at the Inter-bank Foreign Exchange (Forex) market.
It hovered in a range of 68.70 and 68.53 during morning deals before quoting at 68.57 at 1030 hours.
The dollar index was up 0.08 per cent at 96.84 against a basket of six currencies in the early trade.
Overseas, oil prices recovered in Asia today after a steep fall in the previous session, with US crude back above USD 30 a barrel as traders mulled the impact of a potential freeze by key producers.
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The dollar was slightly lower against the yen and the euro
in range-bound afternoon trade today with investors largely avoiding strong positions a day ahead of UK's referendum.
In forward market, premium for dollars remained under pressure due to sustained receivings from exporters.
The benchmark 6-month premium for November dropped to to 183-185 paise compared to 188-190 paise yesterday and far forward May 2017 contract also moved down to 377-379 paise from 382-384 paise.
Meanwhile, the benchmark index Sensex drifted furtner by 47.13 points or 0.18 per cent to end at 26,765.65, while the 50-share Nifty lost 16.20 points to 8,203.70.