Saudi Arabia supports a "fair" solution for the Palestinian cause, King Salman has told Donald Trump in a phone call, as the US President praised the kingdom for opening its airspace to Israel-UAE flights.

Saudi Arabia has said it will not follow the United Arab Emirates, which announced last month it would establish diplomatic ties with Israel, until the Jewish state has signed an internationally recognised peace accord with the Palestinians.

In a phone call to Trump on Sunday, King Salman affirmed the "kingdom's keenness to reach a lasting and fair solution to the Palestinian cause to bring peace", the official Saudi Press Agency reported.

Last week, Saudi Arabia agreed to permit UAE flights to "all countries" to overfly the kingdom, as Israeli premier Benjamin Netanyahu announced the launch of regular direct flights linking the UAE with the Jewish state.

The announcement came just days after the first direct commercial flight from Tel Aviv to Abu Dhabi passed through Saudi airspace, marking the normalisation of Israel-UAE ties under a US-backed deal known as the Abraham Accords.

Riyadh's decision marked another concrete sign of Saudi Arabia's cooperation with Israel even after it publicly refused to follow the UAE's move.

"President Trump... welcomed the opening of Saudi air space to flights between Israel and the United Arab Emirates, beginning with last week's historic commercial flight from Tel Aviv to Abu Dhabi," said a White House readout of the phone call.

"President Trump highlighted the significance of Abraham Accords and discussed ways to enhance regional security and prosperity."

Allowing flights between Israel and the Emirates to cross Saudi airspace saves long detours around the Arabian peninsula.

Saudi Arabia, the Arab world's biggest economy and home to Islam's holiest sites, faces more sensitive political calculations than the UAE.

Despite its clandestine relations with Israel, a formal recognition of the Jewish state would be seen by Palestinians and their supporters as a betrayal of their cause and hurt the kingdom's image as the leader of the Islamic world, analysts say.

Trump also urged Saudi Arabia to "negotiate with other Gulf countries" to resolve a regional rift with Qatar, the White House added.

Riyadh and its allies severed ties with Doha in a shock move in 2017, accusing the gas-rich emirate of backing extremists and siding with Saudi Arabia's regional rival Iran. Qatar denies the charges.

The crisis shows no sign of relenting despite rising international pressure.