Brent crude futures were down 23 cents, or 0.4%, at $63.23 a barrel by 0054 GMT. Prices rose 1.6% last week.
U.S. West Texas Intermediate crude was down by 12 cents, or 0.2%, at $56.08 a barrel. WTI gained 1% last week.
An emergency meeting with parties to Iran's 2015 nuclear deal was constructive but there are unresolved issues and Tehran will continue to reduce its nuclear commitments if Europeans fail to salvage the pact, Iranian official Abbas Araqchi said on Sunday.
"The atmosphere was constructive. Discussions were good. I cannot say that we resolved everything, I can say there are lots of commitments," Araqchi, the senior Iranian nuclear negotiator, told reporters after the meeting in Vienna.
The meeting did not include the United States, which pulled out of the agreement in May 2018 and slapped sanctions back on Iranian oil exports.
Still, tensions remain high around the Strait of Hormuz, the world's most important oil passageway, as Iran refused to release a British-flagged tanker it seized but granted India consular access to 18 Indian crew members.
Denmark welcomed the British government's proposal for a European-led naval mission to ensure safe shipping through the strait.
The United States is also working on a multinational maritime security initiative in the Gulf.
Traders and investors are also focussed this week on meetings of major central banks including the U.S. Federal Reserve, which is expected to lower interest rates.
U.S. economic growth slowed less than expected in the second quarter with a boom in consumer spending, strengthening the outlook for oil consumption.
Growth outside the United States is slowing faster due partly to the impact of the U.S.-China trade war. Senior U.S. and Chinese negotiators are meeting this week for the first time since trade talks broke down in May. A positive outcome may boost crude prices, analysts said.