West Texas Intermediate for February delivery jumped 88 cents to $62.61 a barrel at 11.58am on the New York Mercantile Exchange after touching $62.80. Brent touched $68.27 last week, its highest since May, 2015. Last month's report showed a forecast for 2018 record US crude output of 10 million barrels a day.
Mr. Trump's decision comes on the heels of antigovernment protests in Iran last week, which also boosted the price of crude.
Many producers, still suffering from a 2014 price collapse, are enjoying the rally, although they are wary it will spur rival supply sources.
A key United States government report on Wednesday is expected to show crude stockpiles dropped for an eighth straight week.
Oil prices have received general support from production cuts led by OPEC and a group of non-OPEC producers led by Russian Federation, which started last January, and are set to last through 2018, as well as from strong economic growth and financial markets.
Supply reports this week from industry group the American Petroleum Institute and the US government's Energy Information Administration are expected to show USA crude stocks fell 3.9 million barrels, an eighth week of decline.More news: Apple vows new parental controls amid child addiction fears
"We expect oil demand growth to outpace non-OPEC supply growth in both 2018 and 2019", Standard Chartered analysts said in a note.
Traders said political tensions in Iran, the third-largest producer in the Organization of the Petroleum Exporting Countries, had pushed prices higher. Economic collapse is leading to involuntary production cuts in Venezuela, another OPEC member. OPEC and 10 members outside the cartel agreed late last year to extend an accord to hold down crude output by almost 2% through the end of this year. The price of Brent has risen roughly almost 30% over the past year.
Some in OPEC are anxious a prolonged rally could stimulate more USA shale oil output, however, creating more oversupply that could weigh on prices and market share.
Traders said the gains were due to a slight decline in the number of USA rigs drilling for new production, which eased by five in the week to January 5, to 742, according to data from oil services firm Baker Hughes.
The EIA forecast that USA crude oil production will average 10.3 million barrels per day in 2018 and 10.8 million barrels per day in 2019, breaking historical records for annual average production.
Futures advanced 0.5 percent on Monday, settling near $62 a barrel in NY.