New York's main oil futures contract, light sweet crude for August delivery, fell 1.52 dollars to 143.77 dollars a barrel from Thursday's close of 145.29. US markets were closed Friday for the Independence Day holiday.
Brent North Sea crude for August delivery fell 10 cents to 144.32.
"There is some kind of relaxing on the part of Iran," said Tony Nunan, a manager with Mitsubishi Corp's international petroleum business in Tokyo.
"So any kind of reduction in tension there will take some of the price pressure off," he said.
Driven partly by international tensions over Iran, oil broke a series of price records last week, continuing the momentum begun at the start of the year when it pushed through 100 dollars for the first time.
The price surge has triggered fears about inflation and slower economic growth, while sparking protests around the world.
Iran on Saturday offered to negotiate on its nuclear drive but without a freeze on uranium enrichment, in its first comments since responding to an international package aimed at ending the standoff.
Six world powers are offering Iran technology and negotiations if it suspends uranium enrichment, which the West fears could be used to make atomic weapons. Iran is the world's number four crude producer.
While Iran offered to negotiate, its military chiefs warned that the Islamic republic would shut down the Strait of Hormuz, which is vital for oil exports, and use "blitzkrieg tactics" in the Gulf if it came under attack.
However, Iran's armed forces joint chief of staff stressed his country's priority was that the Strait of Hormuz remains open.
Speculation has been rife that Israel could be planning a military strike against Iranian nuclear sites.
The United States and Japan called Sunday for urgent action on red-hot oil and food prices that could derail the global economy.
Japanese Prime Minister Yasuo Fukuda said he and US President George W. Bush agreed on the need for urgent efforts to tackle the issue. Both are attending the G8 summit which began in Japan earlier Monday.
