The rupee was trading down by 58 paise at 67.83 against the American currency in late morning deals.
Overseas, China's yuan fell to its weakest level against dollar in more than five years after Britain voted to leave the European Union, threatening the existence of the entire bloc and its single currency.
The British pound slumped more than 7 per cent against the dollar as turmoil came to the world markets.
Sustained bouts of dollar demand from importers amid weakness in other Asian currencies also weighed on the rupee, forex dealers said.
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The Indian unit opened sharply lower by 63 paise at 67.88 against yesterday's closing level of 67.25 at the Interbank Foreign Exchange (Forex) market.
It continued the slide and breached the 68-level to hit a low of 68.21 on heavy demand for the American currency from importers and foreign fund outflows as leads show 'Leave' camp ahead in 'Brexit' referendum vote.
Meanwhile, domestic bourses made a smart recovery on
value buying and good earnings visibility amid some short-covering ahead of F&O expiry.
The flagship BSE Sensex rose 101.90 points to close at 28,179.08, while broader Nifty edged higher 16 points to 8,708.95.
In the forward market, premium for dollar turned lower owing to sustained receiving by exporters.
The benchmark six-month premium for March moved down to 151.75-152.50 paise from 152.5-154.5 paise and the forward-September 2017 contract also declined to 327.75-328.75 paise from 328-330 paise last Friday.