The leaders spoke by phone following a historic US-brokered accord last month under which the United Arab Emirates agreed to become the third Arab state to normalise ties with Israel, after Egypt and Jordan, the state news agency reported.
King Salman also told Trump that he appreciated US 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, reports The Guardian.
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 hoped another Arab country normalised ties with within months.
No other Arab state has said so far it is considering following the UAE.
King Salman’s son, 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.
Also read: Palestinians say UAE deal hinders quest for Mideast peace