"Anyone doing business with Iran will NOT be doing business with the United States", he added.
Markets also anticipated an announcement from Washington later on Monday on renewed U.S. sanctions against major oil exporter Iran. These sanctions did not include Iran's oil exports.
USA sanctions on Iran's energy sector are set to be re-imposed after a 180-day "wind-down period" ending on November 4.
Sanctions that went into force on Tuesday target Iran's access to the US dollar, its trade in gold and other precious metals, and other financial measures tied to the national currency, the rial.
He said: "The Iran sanctions have officially been cast".
U.S. West Texas Intermediate (WTI) crude futures were up at 69.21 dollars a barrel.
Many countries, including US allies in Europe as well as China and India, oppose the sanctions, but the USA government said it wants as many countries as possible to stop buying Iranian oil.
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French bank Societe Generale said there was now a "comfortable supply" in physical crude markets, but noted, "Iran sanctions will take another one million bpd off the markets".
"The market continues to price in geopolitical risk from the reimposition of sanctions by the USA on Iran", said Gene McGillian, vice president of market research at Tradition Energy in Stamford, Connecticut. "The reports that Saudi Arabia's production actually dropped in July continue to provide support for the market".
HEAT IMPACTS OIL The main oil market price drivers of recent months have been output levels by top producers Russia, Saudi Arabia and the United States, renewed Iran sanctions, the US-China trade dispute, and unplanned supply disruptions.
Additionally, there are also reports that many USA shale oil drillers posted disappointing quarterly results in recent weeks, hit by rising operating costs, hedging losses and a drop in crude prices away from 2018 highs reached between May and July.
USA crude stockpiles were expected to have dropped 3.3 million barrels last week. US Eastern time (0401 GMT) on Tuesday.
Still, with Russian Federation, the United States and Saudi Arabia now all producing 10 million to 11 million bpd of crude, just three countries now meet around a third of global oil demand.
Also supporting prices were a weakened dollar, McGillian said.
This mostly impacts demand for power fuels such as thermal coal and natural gas.