Trump, who is spending the weekend at his golf property in New Jersey, said in a tweet on Saturday that Custodian of the Two Holy Mosques King Salman bin Abdulaziz Al Saud of Saudi Arabia had agreed to produce more oil.
Russian Federation and Saudi Arabia will face "dire consequences" if they increase their oil production, the head of the state energy firm said.
First Vice President Es'haq Jahangiri said on Monday that Iran is able to counter the looming US sanctions, noting that those at the White House who think they can halt Iran's oil export are living in "illusion". They also stressed on the importance of providing supplies when necessary to "achieve common interests and stimulate the global economic growth".
He explained that it was hard to anticipate how the market would integrate with a possible increase in crude oil output from major producers, referring to Saudi Arabia and Russian Federation.
They agreed to bring down overcompliance with the cuts, resulting in an output increase of one million barrels a day, according to the Saudi energy ministry. The move partly reversed the original OPEC+1 deal which came into force in January past year and was created to reduce the global glut in oil.
Oil is surging as the US pushes allies to end imports of Iranian crude, as global supply disruptions persist and American crude inventories are already at the lowest since January.
"We are working to minimize disruptions to the global market, but we are confident there is sufficient global spare oil capacity", Hook said.
Earlier in the day, Iranian President Hassan Rouhani lashed out at American officials for threatening to stop Iran's oil exports, saying they would never be able to carry out such a threat.
Saudi Arabia's output is up by 700,000 barrels per day (bpd) from May, a Reuters survey showed, and close to its 10.72 million bpd record from November 2016.
On Tuesday, Morgan Stanley raised its Brent forecast to US$85 per barrel, from US$77.5, citing concerns that the United States may succeed in blocking much of Iran's 2.7 million barrels per day. This will include allowing private companies to directly export the oil.
"It depends on the conduct of other governments", Bolton said.
Some major importers of Iranian crude have sent mixed signals on their willingness to abide United States sanctions, particularly as inventories remain low.