In morning trading in New York, benchmark oil for July delivery was up 87 cents to USD 95.63 a barrel.
The oil market's initial reaction to the report from the Labor Department was negative. Oil fell as low as USD 93.72 a barrel after the jobs numbers came out. But US stock markets rose about 1 per cent in early trading, and oil soon reversed course.
US employers added 175,000 jobs in May, below the more robust pace that took place during the fall and winter.
The report also showed the economy added 12,000 fewer jobs in April and March than originally estimated.
Meanwhile, Brent crude, a benchmark for many international oil varieties, was up 69 cents to USD 104.30 a barrel on the ICE Futures exchange in London.