"Saudi Arabia oil supply was attacked. There is reason to believe that we know the culprit, are locked and loaded depending on verification, but are waiting to hear from the Kingdom as to who they believe was the cause of this attack, and under what terms we would proceed! " Trump wrote on his Twitter account on Sunday, Efe news reported.
The president failed to specify who the US intelligence agencies believe was behind the attacks.
Yemen's Houthi rebels, which are backed by Iran, have claimed responsibility for the attacks.
The Shia militia has been engaged in a protracted civil war against the internationally-recognized Yemeni government, which has the military support of a Saudi-led coalition.
On Saturday, US Secretary of State Mike Pompeo directly blamed Iran and said there was no evidence to suggest that the attacks were actually carried out from Yemen.
Authorities in Saudi Arabia were still investigating the attack and have yet to identify a culprit.
The Iranian government, meanwhile, on Sunday denied any involvement.
The attack came amid speculation that Trump could meet with the Iranian president, Hassan Rouhani, on the sidelines of the upcoming United Nations' General Assembly set to be held in New York City at the end of the month.
In a subsequent tweet, Trump again railed against media reports of this possible diplomatic thaw.
"The Fake News is saying that I am willing to meet with Iran, 'No Conditions,'" he said. "That is an incorrect statement (as usual!)."
Trump also tried to use his favourite social media platform - where he has 63 million followers - to calm the markets down.
"PLENTY OF OIL!" he said in a succinct three-word tweet.
On Sunday, the barrel of Brent crude was trading at $70.98 in the New York futures market, an increase of 18 per cent compared to Friday's closing, when it stood at $60.15 per barrel.
In a previous tweet, Trump said he had authorized the release of the US' strategic oil reserves to guarantee the global fuel supply, which has been severely impacted by the attack on the two Saudi refineries.
"Based on the attack on Saudi Arabia, which may have an impact on oil prices, I have authorized the release of oil from the Strategic Petroleum Reserve, if needed, in a to-be-determined amount sufficient to keep the markets well-supplied," the president said.
"I have also informed all appropriate agencies to expedite approvals of the oil pipelines currently in the permitting process in Texas and various other States," Trump added.
The US has an estimated 630 million barrels of oil hidden underground along the coast of the Gulf of Mexico to be used in the event of a serious disruption to the world's oil supply chain.
This reserve aims to prevent a hypothetical scenario in which a temporary scarcity of oil results in a dramatic rise in prices that could again tank the US economy like it did during the 1973-74 oil crisis, when the oil embargo proclaimed by the Organisation of Arab Petroleum Exporting Countries caused a huge global economic shock and an increase of 400 per cent in the price of crude.