The financial markets are still reeling from Brexit's fallout.
World oil prices rebounded in Asia on bargain hunting but tremors from Britain's shock vote last week to leave the European Union continue to weigh on sentiment.
Financial markets are still reeling from Brexit's fallout as investors sell riskier assets and flock to safe bets amid global economic uncertainty.
Asian stock markets resumed their losses early today, extending another sharp sell-off in Europe and New York.
At around 0330 GMT, US benchmark West Texas Intermediate for delivery in August was up 64 cents, or 1.38 per cent, to USD 46.97 and Brent crude for August gained 60 cents, or 1.27 percent, to USD 47.76 a barrel.
Both contracts closed lower on Monday.
"The turmoil in the financial markets, triggered by the UK referendum results, is keeping the pressure on oil prices, which look set to clock a monthly loss in June," said IG Markets Singapore analyst Bernard Aw.
"The lack of guidance from the UK government and the prospects of a leadership struggle continued to dampen investors' appetite, and this should persist through the week," he told AFP.
British Prime Minister David Cameron quit in the wake of the vote and the race is on to find his successor as party leader who would take over as prime minister.
Former London mayor Boris Johnson and Interior Minister Theresa May are considered to be the front-runners in the leadership race.
Policy makers in Europe are trying to calm global markets but analysts said uncertainty remains.
"Apart from economic considerations, concerns are that the Brexit vote could encourage other EU countries to seek their own referendums, including Netherlands, France, Spain and Greece," DBS Bank said in a note.
It said "this could potentially revisit the EU breakup fears that plagued the region" a few years back.
A strengthening US currency -- considered a safe investment in times of turmoil -- will likely continue to dampen demand for dollar-priced oil which would become more expensive for holders of weaker units, Aw added.