The sun sets behind an oil pump outside Saint-Fiacre, near Paris, France March 28, 2019. Photograph:( Reuters )
Brent futures were up 26 cents, or 0.4%, at $65.46 a barrel by 0544 GMT. West Texas Intermediate crude was up 40 cents, or 0.7%, at $57.83 a barrel.
Oil prices rose on Monday to extend gains from last week, bolstered as tensions remain high between Iran and the United States after US Secretary of State Mike Pompeo said "significant" sanctions would be announced on Tehran.
Brent futures were up 26 cents, or 0.4%, at $65.46 a barrel by 0544 GMT.
West Texas Intermediate crude was up 40 cents, or 0.7%, at $57.83 a barrel.
US President Donald Trump said last week that he called off a military strike to retaliate for Iran's downing of an unmanned US drone, and he said on Sunday that he was not seeking war with Iran.
But Pompeo also said "significant" sanctions on Iran would be announced on Monday aimed at further choking off resources that Tehran uses to fund its activities in the region.
"There's a very firm tone to trading on well above average volumes," said Michael McCarthy, chief market strategist at CMC Markets in Sydney.
"We've got concerns about the sanctions against Iran, (but) we are seeing a better demand picture because of the actions of central banks, which is benefiting all commodities ... and we have got a weaker US dollar."
Oil is usually priced in dollars, so a weaker greenback makes it cheaper for holders of other currencies.
The US Federal Reserve is expected to cut interest rates soon to bolster the US economy, while the European Central Bank President Mario Draghi last week called for additional stimulus to boost growth.
Oil prices surged last week after Iran shot down a drone that the United States claimed was in international airspace and Tehran said was over its territory.
Amid the escalating tensions, Brent racked up a gain of about 5% last week, its first weekly gain in five weeks, and WTI jumped about 10%, its biggest weekly percentage gain since December 2016.
Trump said he had aborted a military strike on Iran because such a response to Tehran's downing of the unmanned US surveillance drone would have caused a disproportionate loss of life.
Iranian officials told Reuters that Tehran had received a message from Trump through Oman overnight warning that a US attack on Iran was imminent.
Meanwhile, US energy companies last week increased the number of oil rigs operating for the first time in three weeks.
Companies added one oil rig in the week to June 21, bringing the total count to 789, Baker Hughes said in a closely followed report on Friday.