Secretary of State Antony Blinken departed Israel early Wednesday for Saudi Arabia -- the next stop on his latest Middle East tour.

Before boarding his plane in Tel Aviv, Blinken told reporters that Israel has now achieved most of its military objectives in Gaza -- including the elimination of Hamas leader Yahya Sinwar -- but at great cost to Palestinian civilians.

Blinken said it was time to end the conflict, having spent Tuesday meeting with Israeli leaders -- including Prime Minister Benjamin Netanyahu -- and the families of hostages in a bid to revive cease-fire and hostage release talks.

There is now a need to establish whether a post-Sinwar Hamas will be more open to a diplomatic resolution, Blinken said, plus to facilitate more aid into Gaza and to establish a concrete plan for the post-war governance of the territory.

Blinken said such questions would be part of his meetings with other Middle East leaders through this week.

-ABC News' Shannon Kingston

During their meeting Tuesday, Secretary of State Antony Blinken asked Israeli Prime Minister Benjamin Netanyahu about reports that some Israeli officials wanted to seize control of north Gaza using controversial methods, according to a senior U.S. administration official.

Coined the "General's Plan" by media outlets, the idea would be to force evacuations of the area and assume anyone who stays behind is an enemy combatant and can be fired upon and starved.

The senior U.S. administration official said Blinken noted in the meeting that there's a "perception" that this method is official Israeli policy.

The official said Netanyahu and his top aide, Ron Dermer, denied that it was and said the perception was "deeply damaging" to their efforts.

"We did hear a very clear commitment that that is not their state of policy," the official told a reporter.

-ABC News' Shannon K. Kingston

U.S. Secretary of State Antony Blinken met with Israeli Prime Minister Benjamin Netanyahu for over 2 1/2 hours on Tuesday, as the U.S. makes a push for a cease-fire agreement to end Israel's conflicts with Hamas and Hezbollah.

Blinken and Netanyahu discussed the need to capitalize on the killing of Hamas leader Yahya Sinwar to reach an agreement that would secure the release of the remaining hostages being held in Gaza and putting in place a plan that provides lasting peace for Palestinians and Israelis.

Blinken also discussed the importance of increasing the flow of aid being allowed into Gaza. The U.S. warned Israel last week that assistance could be withheld if humanitarian aid doesn't reach civilians in Gaza.

Lebanon's Rafik Hariri University Hospital will continue providing care despite the building sustaining "severe material damage" in an Israeli strike on Monday, according to Dr. Jihad Saadeh, the head of the hospital.

"Because of the targeting that has happened, we have sustained severe material damage to the hospital, including the destruction of solar panels, extensive destruction of all glass facades and damage to the hospital walls. Severe damage because it seems the shrapnel was very large," Saadeh said.

"We will not stop. Several entities even called me yesterday asking if I would like to evacuate the hospital. I told them, not at all. We will not evacuate. There is no hospital left but us. After the sinful targeting of the suburb’s hospitals, there is no one left except for us. So we will continue our work, God willing," Saadeh said.