Trump described the United States as "locked and loaded" and ready to respond.
Trump has yet to definitely state that Iran was behind the weekend attack, but others in his administration, including Pompeo, have pinned the blame on Tehran. Saudi Arabia is the world's leading oil exporter.
A spokesman for the Iranian president said the Saudis were misguided in their claims.
Washington and its Gulf Arab allies also want Iran to stop supporting regional proxies, including the Houthis who have been battling a Saudi-led military coalition in Yemen for four years.
France's top diplomat is expressing doubt at claims by Yemen's rebel Houthis that they are responsible for recent drone attacks on Saudi Arabian oil facilities.
The Saudi Defense Ministry displayed videos and photographs of alleged Iranian weapons it said were used in the attacks during a news conference on Wednesday.
Seth Jones, a counterterrorism expert at the Center for Strategic and International Studies, said "almost no state" could have fully thwarted such an unconventional attack.
A USA official told Reuters the strikes originated in southwestern Iran.
Later Vice President Mike Pence echoed Trump's comments in a speech saying, "We are locked and loaded, and we are ready to defend our interests", according to USA Today.
Iran sent a note to the US via Swiss diplomats in Tehran on Monday, reiterating that Tehran denies being involved in the Saudi attack, IRNA reported. The shutdown of Abqiaq is the clearest signal possible from Islamic Republic that, as it has stated on several occasions, if the United States insists on depriving it from being able to sell oil, it will not allow the rest of the world's oil to pass through the Strait of Hormuz.
They did not hit the Sanaa bazaar.
Iran's Supreme Leader Mocks 'Confused' U.S. After Trump Negotiation Claims
Iran's Foreign Ministry spokesman Abbas Mousavi dismissed Washington's accusations, calling them "blind and futile". Shortly afterward, Trump ordered a military strike against Iran before changing his mind at the very last second .
Gas Prices to Climb After Attacks on Saudi Arabian Oil Industry
According to Bloomberg , global oil prices have risen by the most on record after a strike on a Saudi Arabian oil facility. It was a more subdued start to trading on Tuesday, with both Brent and West Texas Intermediate futures edging lower.
Storm Humberto hits the Bahamas
With Hurricane Humberto expected to skirt the Carolinas, forecasters say a new system could form. The hurricane center's projected path takes the system north of the Lesser Antilles, however.
French Foreign Minister Jean-Yves Le Drian said Thursday (Sept 19) that a claim by Yemeni rebels that they carried out attacks on two Saudi oil facilities "lacks credibility".
Saudi Arabia has multiple batteries of advanced U.S. Patriot air defense missiles, which are meant to shoot down hostile aircraft or shorter-range ballistic missiles.
The attack on Saudi Arabia's largest oil processing plant disrupted more than half of its daily exports, and was the worst disruption to global crude supplies on record.
When Lindsey Graham annoys his ally in the Oval Office: "President Trump engaged in a long-distance debate over Iran with one of his closest allies on Tuesday as Republicans sought to influence the administration's response to the attacks on oil facilities in Saudi Arabia over the weekend".
France, which is trying to salvage an global nuclear deal with Iran that Washington quit past year, said it wanted to establish the facts before reacting.
The latest incident comes at a time of heightened tensions between Iran and the US following a summer of provocative actions from both sides.
Trump's administration is considering responses including a cyber attack or a physical strike on Iranian oil infrastructure or its Revolutionary Guards, NBC News reported, citing unnamed USA officials.
Mr Feierstein said Saudi Arabia would not want to be drawn into a war either and has been reluctant to point fingers at Iran as it "will be very hard to walk away from possible retaliation" if they do. Oil prices fell after the Saudi reassurances, having surged more than 20 per cent at one point on Monday, the biggest jump since the 1991 Gulf War.
But any firm and strong collective reaction must greatly change the equation and make Iran consider a thousand times before repeating such attacks against world security and stability.
The United States was apparently taken by surprise when when Iran shot down a high-altitude but slow-moving US prototype naval variant of the 737-size Global Hawk surveillance drone with a 3rd Khordad missile variant of the Ra'ad surface to air missile system first deployed a few years ago. But antagonism returned when Trump pulled out of the deal, reached before he took office, and reimposed sanctions, severely damaging the Iranian economy.
Concrete evidence showing Iranian responsibility, if made public, could pressure Saudi Arabia and Washington into a response, though both nations have stressed the need for caution.
Asked in Los Angeles whether Rouhani will come to New York, Trump said, "I really don't know".