Benchmark Brent crude futures were down 34 cents, or 0.5%, at $64.52 a barrel by 0639 GMT. They dropped 0.5% on Monday.
U.S. crude futures were down 24 cents, or 0.4%, at $57.66 a barrel. The U.S. benchmark rose 0.8% in the previous session.
Brent climbed 5% last week and U.S. crude surged 10% after Iran shot down a U.S. drone on Thursday in the Gulf, adding to tensions stoked by attacks on oil tankers in the area in May and June. Washington has blamed the tanker attacks on Iran, which denies having any role.
U.S. President Donald Trump targeted Iranian Supreme Leader Ayatollah Ali Khamenei and other top Iranian officials with sanctions on Monday, taking an unprecedented step to increase pressure on Iran after Tehran's downing of the drone.
"This would appear to effectively rule out any talks or negotiations to end the crisis," said Tom O'Sullivan, founder of energy and security consultancy Mathyos Advisory.
Trump also said on Twitter that other countries should protect their own oil shipping in the Middle East rather than have the United States protect them.
Some said the threat of immediate military conflict had eased slightly.
"Traders have lessened their odds for an immediate U.S.-Iran escalation in this forever smouldering hot spot," said Stephen Innes, managing partner at Vanguard Markets in Bangkok.
Meanwhile, hopes are waning for progress in Sino-U.S. trade talks at this week's G20 meeting as investors await a meeting between Trump and Chinese President Xi Jinping. That could further hurt global growth prospects, hitting demand for oil and other commodities.
"I am not hopeful for U.S.-China," said O'Sullivan, adding that "a compromise might be to delay imposition of 25% tariffs on the $325 billion of imports," that Trump is threatening.
Weak manufacturing data released on Monday by the Federal Reserve Bank of Dallas added to worries about slipping demand for crude oil.
However, supply is expected to remain relatively tight, as the Organization of the Petroleum Exporting Countries and its allies including Russia, an alliance known as OPEC+, appear likely to extend a deal on curbing output when they meet on July 1-2 in Vienna, analysts said.
Russian Energy Minister Alexander Novak said on Monday that international cooperation on crude production had helped stabilise oil markets and was more important than ever. He also voiced concerns about demand.
Sanctions on Iran and Venezuela imposed by Washington have cut oil exports from the two OPEC members but U.S. production has been rising, leading some Russian officials to accuse Washington of carving out market share for its energy exports.