Mr Trump said on Twitter that the US was waiting to hear from the Saudis as to who they believe was behind the attack and “under what terms we would proceed!”
Yemen's Iranian-backed Houthi rebels claimed to have carried out the attack on the world's largest oil processing plant on Saturday, but Washington has blamed Iran itself.
The US released new evidence to back up its allegation that Iran was responsible for the assault amid heightened tensions over Tehran’s collapsing nuclear deal.
What is the new evidence?
The Saudis have been at war with the Houthi rebels since early 2015.
Yet senior US officials said satellite imagery and other intelligence showed the strike was inconsistent with one launched from Yemen, where Houthi rebels had claimed responsibility.
Officials said the photos show impacts consistent with the attack coming from the direction of Iran or Iraq, rather than from Yemen to the south.
What do the satellite images show?
The following satellite images show the damage done to the Abqaiq plant and its Khurais oil field after huge fires broke out.
The drone attack led to the interruption of an estimated 5.7 million barrels of the kingdom's crude oil production per day, equivalent to more than 5% of the world's daily supply.
The drone strike on Abqaiq: Before
The drone strike on Abqaiq: After
The drone strike on Khurais: Before
The drone strike on Khurais: After
How has the war of words escalated?
Iran called Washington’s claims “maximum lies,” while a commander in its paramilitary Revolutionary Guard reiterated its forces could strike US military bases across the Middle East with their arsenal of ballistic missiles.
Earlier, Mr Trump said he had approved the release of US strategic petroleum reserves “if needed” to stabilise energy markets after the attack on Saudi Arabian facilities.
The US president tweeted the attacks could have an impact on oil prices and the final amount of the release, if any, would be “sufficient to keep the markets well-supplied”.
Mr Trump’s tweets followed a National Security Council meeting at the White House that included Vice President Mike Pence, Secretary of State Mike Pompeo and Defense Secretary Mark Esper.
A US official speaking on condition of anonymity said all options, including a military response, were on the table, but added that no decisions had been made.