The leaders spoke by phone following a US brokered accord last month under which the United Arab Emirates agreed to become the third Arab state to normalize ties with Israel after Egypt and Jordan.
King Salman told Trump 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, Reuters reported.
Under the proposal, Arab nations have offered Israel normalized 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 does not recognize 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 following the UAE.
The UAE-Israel deal was met by overwhelming Palestinian opposition.