Brent crude futures fell $1.01 a barrel to $65.47 by 1:04 p.m. EDT (1704 GMT). The international benchmark hit a session high of $67.09 earlier in the day.
West Texas Intermediate crude futures fell by $1.11 a barrel to $58.47. The US benchmark hit a session high of $60.06 earlier.
"What were tailwinds have become headwinds," said Bob Yawger, director of energy futures at Mizuho in New York. He said the same tensions between the United States and Iran that had driven prices higher earlier in the session were putting a damper on the market after Trump's comments.
Trump said on Tuesday a lot of progress had been made with Iran and that he was not looking for regime change in the country.
Trump, who made the remarks at a Cabinet meeting in the White House, did not give details about the progress, but US Secretary of State Mike Pompeo said at the meeting Iran had said it was prepared to negotiate about its missile program.
Tension between the United States and Iran over Tehran's nuclear program have previously lent support to oil futures, given the potential for a price spike should the situation deteriorate.
Uncertainty about China's economic prospects also pressured prices lower after data on Monday showed that growth in the country slowed to 6.2pc from a year earlier, the weakest pace in at least 27 years.
Additionally, US oil companies on Monday began restoring some of the nearly 74pc of production that was shut at platforms in the Gulf of Mexico because of Hurricane Barry.
Workers were returning to the more than 280 production platforms that had been evacuated. It can take several days for full production to resume.
The storm will probably result in a noticeable decline in US crude oil stocks this week, analysts at Commerzbank said.
Inventory data will be published by the American Petroleum Institute on Tuesday evening, and by the US Department of Energy on Wednesday.
However, some say the bullish inventory data is structural, and not attributable only to the storm.
"Beyond the storm we feel we're in a tightening inventory mode through August," said Phil Flynn, an analyst with Price Futures Group in Chicago.