The Saudi military has claimed the attacks were “unquestionably sponsored by Iran” and the US has also indicated it believes Tehran was responsible.
The UK has so far not apportioned blame for Saturday’s attacks, which struck the world’s biggest oil processing facility as well as an oil field and have caused turbulence in world markets.
A Number 10 spokesman said: “The prime minister spoke to president Trump this afternoon following Saturday’s attacks on the Aramco oil facilities in Saudi Arabia.
“They condemned the attacks and discussed the need for a united diplomatic response from international partners.
“They also spoke about Iran and agreed that they must not be allowed to obtain a nuclear weapon.”
The two leaders also briefly discussed Brexit and looked forward to the UN General Assembly meeting in New York next week.
The Saudis have claimed the attack came “from the north” and was “unquestionably sponsored by Iran”.
Military spokesman Colonel Turki al-Maliki did not elaborate, but to the north across the Persian Gulf are Iraq and Iran.
The military also showed journalists what they described as an Iranian cruise missile and drones used in the attack.