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NYMEX crude for March delivery was up 11 cents, or 0.2 per cent, at $61.45 a barrel by 0101 GMT, after settling up 74 cents on Thursday.
For the week, the contract has risen nearly 4 per cent after losing nearly 10 per cent last week.
The move comes at a time when Asian demand is on the rise. India imported a record 4.93 million bpd in January to feed its expanded refining capacity and meet rising demand, data showed.