President Donald Trump and Saudi King Salman want to "rigorously" enforce the Iran nuclear deal, the White House said Sunday, despite the US leader's long opposition to the agreement.

The pair, in a phone conversation, also spoke of the need to address Iran's "destabilizing regional activities," fight the spread of "radical Islamic terrorism" and establish safe zones in war-ravaged Syria and Yemen, the White House statement read.

No further details were provided about those plans.

The official Saudi Press Agency early on Monday confirmed that Trump had called Salman.

It made no mention of Iran but said the views of the two leaders "were identical" on issues discussed during the call, including "confronting those who seek to undermine security and stability in the region and interfere in the internal affairs of other states."

Riyadh regularly accuses Tehran of regional interference.

SPA said Trump and Salman also agreed on "formulating the appropriate mechanisms" for countering "terrorism" and extremism.

Trump opposed the nuclear agreement signed by Israel's arch-foe Iran and world powers, including the United States, in 2015 and has said he wants to undo it.

Some of his key nominees have adopted an openly anti-Iran stance, including secretary of state candidate Rex Tillerson, who is seeking a complete revision of the accord.

Israeli President Benjamin Netanyahu said last month that there were many ways of "undoing" the Iran nuclear deal and that he would discuss that with Trump.

But before he left office, former president Barack Obama warned against rowing back the pact, emphasizing its "significant and concrete results."

The deal places curbs on Tehran's nuclear program in exchange for the lifting of international sanctions.

Tehran is a major foe of both Washington and Riyadh. The Sunni majority Saudi kingdom is engaged in a power struggle with the Shiite country for dominance in the region.

Salman and Trump invited each other to visit their respective capitals, the Saudi Press Agency said.

"The two leaders agreed to schedule the visits in the coming period", it said.

The United States and Saudi Arabia have a decades-old relationship based on the exchange of American security for Saudi oil.

But ties between Riyadh and Washington became increasingly frayed during the eight-year administration of former president Barack Obama.

Saudi leaders felt Obama was reluctant to get involved in the civil war in Syria and other regional conflicts.

Riyadh's Foreign Minister Adel al-Jubeir has said he expects the Trump administration to be more engaged in the Middle East, and the world in general, while "rebuilding" relationships with allies.

Trump and King Salman "agreed on the importance of rigorously enforcing the Joint Comprehensive Plan of Action with Iran and of addressing Iran's destabilizing regional activities," the White House said.

Trump also spoke by telephone with the crown prince of Abu Dhabi, Mohammed bin Zayed Al Nahyan, committing to "further strengthen cooperation on fighting radical Islamic terrorism," the White House said.

It said the pair also discussed establishing safe zones for refugees displaced by conflict in the region, and the crown prince "agreed to support this initiative."