The leaders spoke by phone following a historic U.S. brokered accord last month under which the United Arab Emirates agreed to become the third Arab state to make peace deal with Israel after Egypt and Jordan.
King Salman told Trump he appreciated U.S. efforts to support peace and that Saudi Arabia wanted to see a fair and permanent solution to the Palestinian issue based on the Arab Peace Initiative proposed by the kingdom in 2002.
Under the proposal, Arab nations have offered Israel normalised ties in return for a statehood deal with the Palestinians and full Israeli withdrawal from territory captured in the 1967 Middle East war.
Saudi Arabia, the birthplace of Islam and site of its holiest shrines, does not recognise Israel.
However, this month the kingdom said it would allow flights between UAE and Israel, including by Israeli airliners, to use its airspace.
White House adviser and Trump son-in-law Jared Kushner has said he hopes another Arab country normalizes ties with within months.
No other Arab state has said so far it is considering a peace deal with Israel.
Saudi Crown Prince Mohammed bin Salman and Kushner discussed the need for the Palestinians and the Israelis to resume negotiations and reach a lasting peace after Kushner visited the UAE last month.
The UAE-Israel deal was met by overwhelming Palestinian opposition.
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