Gallant also stressed to Sullivan the importance of ensuring that Israel maintains its strategic military edge.
Sullivan arrived in Israel Sunday from Saudi Arabia where he met with Crown Prince Mohammed bin Salman.
The White House said on Friday that Sullivan would visit Saudi Arabia and Israel to discuss bilateral and regional matters, including Gaza and efforts to achieve lasting peace and security in region.
John Kirby said Sullivan's talks with Netanyahu and other senior Israeli officials will include Rafah.
It is crucial that Israel clearly and loudly communicates to Sullivan the drawbacks of the proposed normalization and the defense pact and does not rush into signing.
Friday's meeting with Sullivan was also the first time the families met with the White House after Hamas released videos of three hostages, including Americans Keith Siegel and Hersh Goldberg-Polin.
The representatives said they fear US public disputes with Israel only emboldens mutual enemies like Hamas, Hezbollah, the Houthis and other Iranian-backed proxies.
The US has opposed a Rafah ground invasion because it fears it would create a humanitarian disaster, but Prime Minister Benjamin Netanyahu has insisted that he plans to move forward
Israeli-American hostage families met White House officials, discussing safety and release hopes. They also addressed efforts to limit Hamas funding.
Although the hopes Israeli-Saudi normalization deal have diminished since the start of the Israel-Hamas war, the Biden administration remains keen on reviving prospects.
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