* U.S. crude stockpiles fell 5.8 mln bbls last week -API
* Libyan rebels agree to open vital oil ports within days
* Weak China, Europe factory data weighs
* Coming up: U.S. EIA weekly oil stocks at 1430 GMT
SINGAPORE, April 2 (Reuters) - Brent crude steadied above $105 a barrel on Wednesday but was still near a five-month low, with investors waiting for more U.S. inventory data to assess demand in the world's largest oil consumer.
Oil tumbled 2 percent on Tuesday after Libyan rebels said they would re-open vital oil ports within days, while poor manufacturing data from China and Europe weighed on the outlook for fuel demand.
May Brent crude had inched up 4 cents to $105.66 a barrel by 0257 GMT, after settling at its lowest since Nov. 11.
U.S. crude for May delivery was up 2 cents to $99.76 a barrel, after a 1.8-percent drop to its lowest settlement since March 26 on Tuesday.
"The market needed to correct after strong gains since mid-March," said Ken Hasegawa, a commodity sales manager at Newedge Japan. "It's possible that Libyan exports triggered a sell-off."
A rebel group in eastern Libya has agreed with the government to end its seizure of vital oil ports, a senior leader told Reuters, raising hopes for an end to an eight-month stalemate that has dried up state income and fuelled chaos.
A Reuters survey showed on Tuesday that OPEC's oil output fell in March to its lowest since December as Iraq's oil revival suffered a setback and outages cut output in African producers.
U.S. crude pared losses after industry data showed crude stockpiles fell significantly last week against analyst expectations for a build.
Crude inventories dropped 5.8 million barrels in the week to March 28 to 373.5 million barrels, data from industry group the American Petroleum Institute showed on Tuesday, compared with analyst expectations for an increase of 1.1 million barrels.
Crude stocks at the Cushing, Oklahoma, delivery hub fell by 1.5 million barrels, API said. Gasoline inventories increased and distillate stocks fell, it added.
Attention is now turning to inventory data due on Wednesday from the Energy Information Administration.
Newedge's Hasegawa said oil would stay rangebound ahead of key jobs data from the United States this Friday.
"Brent's range will have a floor at $105 and could possibly rebound," said Hasegawa, adding that U.S. crude could stay between $97 and $103.
Geopolitical tensions between Russia and the west over Ukraine simmered, although analysts and traders expect the crisis to have less impact on oil supplies than natural gas.
(Reporting by Florence Tan; Editing by Joseph Radford)