Israeli forces conducted an airstrike on what they claim were Hamas terrorists operating within a command and control center embedded inside a school in Gaza City, Israeli Defense Forces said in a statement Wednesday.

Ten people were killed from the strike, the Hamas-run Gaza Ministry of Health said.

"A short while ago, with the direction of IDF and ISA intelligence, the IAF conducted a precise strike on Hamas terrorists operating within a command and control center embedded inside a compound that previously served as the 'Ibn Al-Haytam' School in the area of Gaza City," the IDF said in a statement.

Saudi Arabian Crown Prince Mohammed bin Salman said the kingdom would not recognize Israel as a state without a Palestinian state.

"The Palestinian cause is at the forefront of your country’s affairs. We renew the kingdom’s rejection and strong condemnation of the crimes of the Israeli occupation authority against the Palestinian people, ignoring international and humanitarian law in a new and bitter chapter of suffering," Prince Mohammed said.

"The kingdom will not stop its tireless work towards the establishment of an independent Palestinian state with East Jerusalem as its capital, and we affirm that the kingdom will not establish diplomatic relations with Israel without that. We extend our thanks to the countries that have recognized the Palestinian state, in accordance with international legitimacy, and we urge the rest of the countries to take similar steps," Prince Mohammed said.

The U.S. and Saudi Arabia had previously paved the way for normalizing relations with Israel before the eruption of the war in the Gaza Strip last October put those plans on hold.

Israel has begun a "new phase in the war," with Israel diverting forces and resources toward northern Gaza, Israeli Defense Minister Yoav Gallant said at the air force's Ramat David base on Wednesday.

"The center of gravity is moving north, the meaning is that we are diverting forces, resources, energy towards the north. We have not forgotten the abductees and we have not forgotten our tasks in the south, this is our duty and we are carrying it out at the same time," Gallant said.

"It is very important to do things at this stage in close cooperation -- between all organizations, at all levels," Gallant said.

Secretary of State Antony Blinken said during a press conference in Egypt on Wednesday that the U.S. "did not know about and was not involved" in Israel's pager attacks in Lebanon and Syria -- but said that officials were still gathering information and did not directly blame Israel.

"Broadly speaking, we've been very clear, and we remain very clear about the importance of all parties avoiding any steps that could further escalate the conflict that we're trying to resolve in Gaza," Blinken said. Its spread to other fronts, he added, is "clearly not in the interest of anyone involved."

Blinken also reaffirmed the Biden administration's commitment to reaching a cease-fire, which he said would "materially improve the prospects of defusing the situation" on the Israeli-Lebanese border and allow thousands of people living near the area on both sides of the divide to return home.

"That's clearly the best path forward for everyone involved. So again, it's imperative that everyone avoid taking steps that could further escalate or spread the conflict," he said.

Egyptian Foreign Minister Badr Abdelatty was also asked about the matter, and had much more to say. He declared, via a translator, that Egypt was "against any unilateral action that attacks the sovereignty of Lebanon."

"We have condemned and we will condemn any targeting of the Lebanese sovereignty," he said. "It does not encourage any civility."

He continued: "Such dangerous escalation can lead to what we have warned of before, which is leading to the edge of a regional war which can kill everyone."

The foreign minister also asserted that the "heart of the crisis" facing the Middle East was "Israeli aggression in Gaza."

-ABC News' Shannon Kingston