Egyptian state-linked media confirmed Saturday evening that the country has deployed equipment and a specialized team to the Gaza Strip to help locate and recover the bodies of Israeli hostages who remain missing.

Hamas leader Khalil al-Hayya also confirmed that “new areas will be entered” on Sunday to search for the bodies of the missing hostages, according to a write-up on Hamas’ official website summarizing Al-Hayya’s interview with Al Jazeera on Saturday.

"We will not give the occupation a pretext to resume the war. ... We have no reservations on any national figure residing in Gaza to administer the Gaza Strip. ... Our weapons are linked to the presence of occupation and aggression; if the occupation ends, these weapons will be transferred to the state," al-Hayya added in the Al Jazeera interview.

-ABC News' Ayat Altawy, Nasser Atta, Jordana Miller and Samy Zyara

Israeli Prime Minister Benjamin Netanyahu used a Sunday cabinet meeting to push back on recent suggestions that the U.S. is dictating security policy on Gaza.

"Israel is an independent state, the United States is an independent state," Netanyahu said.

"The relations between us are those of partners," he said, adding, "I want to make one thing clear -- it is our own security policy. We are not prepared to tolerate attacks against us, we respond according to our own discretion against attacks, as we have seen in Lebanon and in Gaza."

Netanyahu also said Israel is not seeking approval for military attacks and addressed the issue of international teams meant to monitor the ceasefire deal in Gaza.

"We control our own security and we have made it clear to the international forces that Israel will determine which forces are acceptable to us, and that is how we operate and will continue to operate," he said.

-ABC News' Jordana Miller and Victoria Beaule

President Donald Trump pressed Hamas to return the bodies of all deceased hostages or face "action" from nations involved in the Gaza ceasefire plan.

"We have a very strong PEACE in the Middle East, and I believe it has a good chance of being EVERLASTING," Trump wrote in a Saturday social media post.

"Hamas is going to have to start returning the bodies of the deceased hostages, including two Americans, quickly, or the other Countries involved in this GREAT PEACE will take action," Trump added.

The bodies of 13 hostages are still believed to be in Gaza. Hamas committed to returning all living and deceased captives being held in the strip as part of the ceasefire deal reached earlier this month. All 20 living hostages and the bodies of 15 deceased captives have so far been released.

Hamas officials have said the group is continuing to search for the remaining hostage bodies, saying the devastation caused by Israel's attacks on Gaza has complicated recovery efforts.

-ABC News' Hannah Demissie

Secretary of State Marco Rubio has named U.S. Ambassador to Yemen Steven Fagin as the "civilian lead" of the Civil-Military Coordination Center, in charge of monitoring the ceasefire in Gaza.

Fagin, will join the military lead for the operation, Lt. Gen. Patrick Frank, and 200 servicemembers from U.S. Central Command -- with expertise in transportation, planning, security, logistics and engineering -- who are staffing the hub.

Frank briefed Rubio today at the center, according to the television pool.

Rubio promised more diplomats would arrive at the hub, as well as personnel from partner nations who are involved in shoring up the ceasefire between Israel and Hamas.

Trump Administration officials said the hub will have representatives from partner nations, NGOs, international institutions and the private sector to support stabilization efforts.

Vice President JD Vance and Israeli Prime Minister Benjamin Netanyahu are meeting in Tel Aviv, Israel, to discuss American-Israeli partnership, and next steps for the ceasefire between Israel and Hamas.

"These days of destiny" are what Vance and Netanyahu are calling this stage of the Gaza peace plan, hinting at the massive undertaking that must happen to "disarm Hamas" and "rebuild Gaza."

"We have a very, very tough task ahead of us, which is to disarm Hamas but rebuild Gaza to make life better for the people in Gaza, but also to ensure that Hamas is no longer a threat to our friends in Israel," Vance said.

Both leaders also commented on suggestions that either Israel controls the United States -- or that the United States controls Israel. Netanyahu called the assumption "hogwash" and reaffirmed that both the United States and Israel are committed to a "partnership" even if they have "disagreements, here and there."

"We have a partnership, an alliance of partners who share common values, common goals. We can have discussions," he said. "We can have disagreements here and there. But on the whole, I have to say that in the past year, we've had agreement."

Vance added to the prime minister's comments, saying that Israel is not a client or vassal state, but is still committing to the partnership between the United States and Israel. He added that he sees Israel playing a leadership role in the Middle East and North Africa, so that "the United States can care less about the Middle East."

Vance said he remains hopeful that the Israel-Hamas ceasefire will hold, but said that there will be a lot of work ahead.

"It's not easy. I never said it was easy, but what I am is optimistic that the cease fire is going to hold and that we can actually build a better future in the entire Middle East," Vance said.

-ABC News' Alex Ederson and Somayeh Malekian