(Corrects paragraph 2 to show Brent fell 0.5% on Monday, not rose 0.5%; corrects paragraph 3 to show WTI gained 0.8% on Monday, not fell 0.8%)
TOKYO, June 25 (Reuters) - Oil prices were steady on Tuesday, supported by worries over conflict between Iran and the United States but pressured by concerns about a potential decline in demand for crude.
Benchmark Brent crude futures were up 3 cents at $64.89 a barrel by 0034 GMT. They fell 0.5% on Monday.
U.S. crude futures were down 3 cents at $57.87 a barrel. The U.S. benchmark rose 0.8% in the previous session.
Brent rose 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.
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.
But 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 Presidents Donald Trump and Xi Jinping.
Weak manufacturing data released on Monday by the Federal Reserve Bank of Dallas added to worries about slipping demand for crude oil.
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. (Reporting by Aaron Sheldrick; Editing by Joseph Radford)