The king also emphasised the need to advance the peace process in a phone call with U.S. President Donald Trump on Monday night, made after Israeli security forces killed 16 Palestinians last week during a demonstration along the Israel-Gaza border. The number rose to 17 on Tuesday.
King Salman reaffirmed "the kingdom's steadfast position towards the Palestinian issue and the legitimate rights of the Palestinian people to an independent state with Jerusalem as its capital", state news agency SPA said on Tuesday.
Palestinian President Mahmoud Abbas praised King Salman, thanking him for his support.
"President Abbas expressed his gratitude and appreciation ... for his supportive positions of the Palestinian people, the Palestinian cause and the cause of Jerusalem and its sacred sites," said a statement published by the official Palestinian WAFA news agency.
Abbas also praised Saudi Arabia for continuing to support the right of the Palestinian people to establish their independent state with East Jerusalem as its capital, the statement said.
The report did not refer to the comments by Crown Prince Mohammed bin Salman in an interview published on Monday by U.S. magazine The Atlantic, which are the latest public sign that ties between Saudi Arabia and Israel may be growing closer.
"I believe the Palestinians and the Israelis have the right to have their own land. But we have to have a peace agreement to assure the stability for everyone and to have normal relations."
Saudi Arabia, birthplace of Islam and home to its holiest shrines, does not recognise Israel. It has maintained for years that normalising relations hinges on Israeli withdrawal from Arab lands captured in the 1967 Middle East war, territory Palestinians seek for a future state.
Increased tension between Riyadh and Tehran has fuelled speculation that shared interests may push Saudi Arabia and Israel to work together against what they see as a common Iranian threat.
(Reporting By Stephen Kalin; editing by David Stamp and Diane Craft)
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)