Deeming the forging of formal Israeli-Saudi ties a U.S. interest, President Joe Biden's national security adviser, Jake Sullivan, made a May 6-8 shuttle trip to the two countries.

That followed a New York Times report in March that Riyadh - whose relationship with the Biden administration is strained - was conditioning normalisation with Israel on boosted U.S. defence sales and assent for a Saudi civilian nuclear programme.

Saudi officials have not confirmed this. Sullivan's Israeli counterpart, Tzachi Hanegbi, appeared to do so on Tuesday, saying in a interview that the Saudis had raised terms with the United States as part of a "triangular" diplomacy.

Yet Hanegbi hedged on how Israel might respond, saying such Saudi requests were, for now, "an American dilemma".

"I say this to be as clear as I can within the framework of the fog that exists for us, too," he told Israel's Army Radio. "We are not really aware, right now, of what is happening in the Saudi-American corridors."

Any new U.S. weaponry supplied to Saudi Arabia could have to comply with Washington's commitment to preserving an Israeli "qualitative military edge" (QME) in the region, Hanegbi said.

"This is a subject that will be discussed, but only if and when relevant, meaning if indeed the Saudis and Americans reach a breakthrough in their relations," he said.

Hanegbi predicted any Saudi plans for civilian nuclear projects would first have to clear U.S. counter-proliferation regulations meant to prevent any covert push for nuclear arms.

"When the subject becomes relevant to the security of Israel, the Americans will certainly not make progress on it without close contacts" with the Israeli government, he added.

Saudi Arabia, a Middle East powerhouse and home to Islam's two holiest shrines, gave its blessing to Gulf neighbours United Arab Emirates and Bahrain establishing relations with Israel in 2020 under the previous U.S. administration of Donald Trump.

Riyadh has not followed suit, saying Palestinian statehood goals should be addressed first. In April, Saudi Arabia restored ties with Iran, a regional rival and Israel's arch-foe.

Israeli and U.S. officials have voiced hope that, as a stop-gap goodwill measure, the Saudis will admit the first direct commercial flights for Muslims from Israel making the haj pilgrimage next month. Hanegbi sounded circumspect about that.

"We would like for it to happen (but) it is not clear whether, under this schedule, it can happen," he said.