Trump affirmed that Washington is allied with Riyadh and supports the kingdom, stressing what he referred to as the negative impact of attacks on the US and the global economy, according to SPA.
Crown Prince Mohammed bin Salman told Trump during the phone call that "The kingdom is willing and able to confront and deal with this terrorist aggression", according to SPA.
The White House confirmed later on Saturday that Trump had offered support for Saudi Arabia.
"The United States strongly condemns today's attack on critical energy infrastructure [...] Violent actions against civilian areas and infrastructure vital to the global economy only deepen conflict and mistrust", White House spokesman Judd Deere said in a statement on Saturday, adding that the United States was committed to keeping oil markets well-supplied in the wake of the attack on Saudi Arabian oil plants.
Fires hit the Abqaiq oil refinery, a gated production facility and living community in the nation's Eastern Province, as well as an oil-processing facility near the Khurais oil field, located 100 miles east of Riyadh, according to SPA.
The armed Yemeni Houthi opposition movement claimed responsibility for the attacks.
According to a statement from the Houthi armed forces, broadcast by Almasirah TV channel, the group attacked the Abqaiq and Khurais oil refineries with 10 drones, the biggest Houthi operation within Saudi territory to date, according to a spokesperson.
The attacks will continue until Saudi Arabia stops conducting military operations in Yemen, according to the Houthi statement.
Earlier, Houthi armed forces carried out a drone attack on the Shaybah oil field and refinery in Saudi Arabia, prompting a counter-attack by the Saudis on targets in northern Yemen.
Yemen has since 2015 been engulfed in a war between government forces led by exiled President Abdrabuh Mansour Hadi and the rebel Houthi movement.
A Saudi-led coalition has been carrying out airstrikes against the Houthis at Hadi's request since March 2015. Hadi is said to be under virtual house arrest in Riyadh while the kingdom carries out its attacks in Yemen, according to multiple sources.