By Deep Kaushik Vakil and Ahmad Ghaddar

LONDON (Reuters) -Oil prices edged up from four-month lows on Wednesday after a fillip from a U.S. jobs report that firms up the case for a September cut to interest rates while markets weighed OPEC+ plans to begin tapering some output cuts later this year.

futures were up 39 cents, or 0.5%, at $77.91 a barrel by 1241 GMT. U.S. West Texas Intermediate crude futures rose 39 cents, or 0.5%, to $73.64.

Both contracts fell more than 1% on Tuesday to their lowest settlement levels since early February, having declined by about $3 a barrel on Monday.

The slide followed news from the Organization of the Petroleum Exporting Countries (OPEC) and its allies of plans to increase supply from the fourth quarter despite recent signs of weakening demand growth.

“The abundant supply picture at present undoubtedly is generating queasiness even from those not in the perennial OPEC-sceptic camp,” RBC Capital’s head of commodities research, Helima Croft, said in a market note.

However, Saudi Arabian energy minister Prince Abdulaziz bin Salman has said OPEC+ would pause the unwinding of the cuts or reverse them if demand wasn’t strong enough to absorb the barrels.

Prices drew some support from data showing U.S. private payrolls increased less than expected in May, with data for April also revised lower.

This added to Tuesday’s report that U.S. job openings fell more than expected in April, which could help the Federal Reserve’s fight against inflation and strengthen the case for cutting interest rates.

“Yesterday’s U.S. job data hints at a softer labour market and a September rate cut from the Fed,” said PVM Oil analyst Tamas Varga.

The United States could hasten the rate at which it replenishes the Strategic Petroleum Reserve, Energy Secretary Jennifer Granholm told Reuters on Tuesday, adding that she believes that the global oil market is well-supplied.

stocks by increased more than 4 million barrels in the week ended May 31, according to sources citing American Petroleum Institute figures. [API/S]

Analysts polled by Reuters had forecast a 2.3 million barrel decline.

Gasoline stocks rose by more than 4 million barrels, twice the build expected by analysts.

“Renewed inventory draws are needed to push oil prices higher,” said UBS analyst Giovanni Staunovo.

The U.S. Energy Information Administration publishes official stockpile data at 1430 GMT on Wednesday.

Data for last week is being closely watched by markets because it reflects fuel usage around the Memorial Day holiday, the start of the so-called U.S. driving season.