* 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; 1430 GMT
(Updates prices, adds quote)
LONDON, April 2 (Reuters) - Brent crude oil steadied above $105 a barrel on Wednesday after hitting a near five-month low the previous session, as investors waited for U.S. inventory data to assess demand in the world's top oil consumer.
Crude prices on both sides of the Atlantic tumbled nearly 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.
Brent crude oil had inched up 13 cents to $105.75 a barrel by 0942 GMT, after closing at its lowest level since Nov. 11.
U.S. crude oil was down 5 cents to $99.69 a barrel, after dropping 1.8 percent in the previous session.
Data released on Tuesday by the American Petroleum Institute (API) showed crude stocks dropped 5.8 million barrels in the week to March 28 to 373.5 million barrels. Analysts had expected an increase of 1.1 million barrels.
Crude stocks at the Cushing, Oklahoma, delivery hub fell by 1.5 million barrels, the industry group said.
The market is now eyeing oil inventory data due on Wednesday from the U.S. Energy Information Administration (EIA) for more trading cues.
"If the upcoming EIA weekly release were to reveal lower crude inventories consistent with the API data, we are likely to expect prices to retrace upwards," Phillips Futures analyst Tan Chee Tat said in a note.
Tuesday's slump was attributed to news that a rebel group in eastern Libya has agreed with the government to end its seizure of oil ports, raising hopes for an end to an eight-month stalemate that has dried up state income.
However, agreements have been announced in the past, only to fall apart soon after and oil markets have become more cautious.
Surveys showing factories across Europe eased back on the throttle in March and China's vast manufacturing industry contracted for a third straight month also put downward pressure on oil.
"The sharp... reduction in U.S. crude oil stocks reported by the API after close of trading yesterday was... unable to lend any buoyancy to prices. We therefore regard yesterday's price slump as an overreaction and expect the price to recover in the coming days," Commerzbank said in a note to clients.
Estimates for a drop in supply from the Organization of the Petroleum Exporting Countries (OPEC) boosted investor sentiment.
A Reuters survey showed 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.
Despite political tensions between Russia and the West over Ukraine, analysts and traders expect the crisis to have less impact on oil supplies than on natural gas.
(Additional reporting by Florence Tan in Singapore; editing by Jason Neely)