TEL AVIV—Israeli Prime Minister Benjamin Netanyahu secretly met Saudi Arabia’s crown prince in the kingdom on Sunday, according to three Saudi government advisers, in their first known meeting and amid a U.S. push to normalize ties between the longtime foes.

Saudi Arabia has denied the meeting took place, but Israel hasn’t. Conflicting accounts reflect the political sensitivity of warming relations with Israel for Saudi Arabia, which for decades has competed with Iran for the mantle of Islamic leadership. Normalizing ties with Israel before any deal for Palestinian statehood would be a seismic shift in the Middle East, inviting scorn from regional rivals Iran and Turkey and potential protests or militant attacks from conservative Saudis.

Mr. Netanyahu’s meeting with Prince Mohammed bin Salman on Sunday evening in the seaside corner of northwest Saudi Arabia coincided with U.S. Secretary of State Mike Pompeo’s visit. Yossi Cohen, the director of Israel’s spy agency Mossad, accompanied the Israeli prime minister, according to Israel’s Army Radio.

One of the Saudi advisers familiar with the talks told The Wall Street Journal that Mr. Pompeo hadn’t joined the meeting, as Israel’s Army Radio initially reported, but had helped arrange it. Mr. Pompeo met Mr. Netanyahu in Jerusalem during a three-day visit last week.

The Saudi and Israeli leaders discussed several issues, including normalization of ties and Iran, but no substantial agreements were reached, another Saudi adviser said. He said the meeting lasted a couple of hours. One area of focus was on how to coordinate moves to contain Iran once the Biden administration, which has indicated it wants to re-engage with Tehran, takes over, the adviser said.