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US President Joe Biden's national security advisor briefed Benjamin Netanyahu on the "potential" of a normalization deal between Israel and Saudi Arabia after holding talks in the region, the White House said Sunday.

Jake Sullivan also called on the Israeli prime minister to link the military operation against Hamas in Gaza with a "political strategy" for the future of the Palestinian enclave, it said in a readout of the talks.

Defence Minister Yoav Gallant -- who last week slammed the premier for not announcing post-war plans -- said Monday he told visiting US National Security Advisor Jake Sullivan of "Israel's duty to expand the ground operation in Rafah, to dismantle Hamas and to return the hostages".

Sullivan met with Netanyahu on Sunday and told him Israel must link the military operation against Hamas with a "political strategy" for Gaza's future, the White House said.

It added they also discussed the "potential" of a normalisation deal between Israel and Saudi Arabia, where Sullivan held talks before arriving in Israel.

In a weekend of high-stakes diplomacy, Sullivan met Saudi Crown Prince Mohammed bin Salman in Dharan on Saturday, before flying directly to Israel for talks with Netanyahu and other key officials.

"Mr Sullivan briefed Prime Minister Netanyahu and his team on these meetings and the potential that may now be available for Israel, as well as the Palestinian people," the White House said.

Saudi state media reported earlier Sunday that Sullivan and Prince Mohammed, the country's de facto ruler, discussed a "semi-final" version of a deal expected to beef up security ties between their two countries.

That deal is considered a major part of Washington's efforts to bring Riyadh around to a so-called mega-deal recognizing the state of Israel for the first time -- efforts complicated by the ongoing war in the Gaza Strip.

There was no immediate reaction from Israel, which despite relying on Washington for military aide has largely spurned Biden's calls for restraint in Gaza.

While in Israel Sullivan had "reiterated the president's longstanding position on Rafah," the southern Gazan town where Israel is threatening a major offensive, the White House said.

The Biden administration has called on Israel to avoid such an operation and recently halted a shipment of bombs to its longstanding ally due to concerns they might be used in Rafah.

Sullivan also "reaffirmed the need for Israel to connect its military operations to a political strategy that can ensure the lasting defeat of Hamas, the release of all the hostages, and a better future for Gaza", it said.

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