Brent crude climbed towards $104 a barrel on Wednesday after South Korea's sweetened incentives for non-Middle East crude oil imports heightened demand prospects, and fuel stockpiles in the United States declined sharply.

Investors are also watching the dollar, which hit session lows against the euro and yen after a report showed fewer private sector jobs were created in May than expected.

Brent crude rose 39 cents to $103.63 a barrel by 1300 GMT. U.S. oil rose 81 cents to $94.12.

The move by South Korea, the world's fifth biggest oil importer, to cut its reliance on Middle East suppliers and make imports of crude from other regions more attractive is expected to increase demand for crudes priced off Brent.

"It should also make it easier for South Korean refiners to test and import other light grades than just Forties from the Atlantic Basin (eg North and West African crude oils)," said Swiss-based energy analyst Olivier Jakob of Petromatrix.

Brent's premium to Middle East benchmark Dubai rose to the highest in more than two weeks following the development.

Prices were also supported by data from the American Petroleum Institute (API) that showed a surprise 7.8-million-barrel drop in crude stocks in the world's top oil consumer, versus forecasts for a decline of 400,000 barrels.

Market participants are now awaiting oil inventory figures from the Energy Information Administration (EIA), generally considered more reliable, to gauge the demand outlook for the world's biggest economy.

"After the API's data, there are downside risks for the forecasts of a slight crude oil inventory reduction and a gasoline inventory build," said Carsten Fritsch of Commerzbank.

"The plentiful supply, and only subdued growth in demand, nonetheless suggest that prices will struggle to climb much further."

Investors are also watching a string of U.S. jobs data due out this week that started with today's private sector survey from payrolls processor ADP. Weekly jobless claims have been in focus as investors try to second guess U.S. monetary policy.

"These economic indicators have gained a lot of importance of late, and most markets, including oil, are looking at these numbers more than they were before," said Ben Le Brun, an analyst at OptionsXpress in Sydney.

"Overall, oil markets will remain largely choppy as investors try and gauge if stimulus measures from the U.S. Fed will continue or not." (Additional reporting by Manash Goswami and Florence Tan in Singapore; editing by Keiron Henderson)