The Israel-Hamas war "could easily metastasize" beyond the Palestinian territory as "profound tension" in the region raises the prospect of a wider conflict, Secretary of State Antony Blinken said on Sunday during an ongoing trip to the Middle East.

Such fighting would "cause even more insecurity and suffering," Blinken told reporters in Doha, Qatar, alongside Qatari Prime Minister Mohammed bin Abdulrahman Al Thani.

Blinken is roughly halfway through a nine-stop tour around the Middle East, his fourth diplomatic mission since the war began after Hamas' Oct. 7 terror attack on Israel killed 1,200.

Looking ahead to his meetings with Israeli leaders in Tel Aviv and the West Bank set for early this week, Blinken said Sunday, "I will also raise the imperative of doing more to prevent civilian casualties. Far too many Palestinians, innocent Palestinians, have already been killed."

The secretary of state, like other U.S. officials including President Joe Biden, have sought to stress their support for Israel's retaliatory operations against Hamas while calling for Israel to do as much as possible to curb civilian casualties in light of the ongoing onslaught in Gaza and high death toll.

The International Rescue Committee and Medical Aid for Palestine (MAP) said Sunday they were "forced to withdraw and cease activities" at Gaza's Al Aqsa hospital "as a result of increasing Israeli military activity" around the medical facility.

The Israeli military has dropped leaflets designating areas surrounding the hospital as a "red zone," the relief organizations said in a statement.

"Given the recent history of attacks on medical staff and facilities in Gaza, the team is unable to return," the statement said. "Many local health workers have also been unable to access the hospital to care for the hundreds of patients that remain due to the conflict."

A MAP staff member is currently a patient at the hospital after she was injured and her three sisters were killed in an Israeli bombing of a house they were staying in, according to the statement.

ABC News reached out to the Israel Defense Forces for comment.

Doctors Without Borders, or Médecins Sans Frontières (MSF), also said Sunday it was evacuating its staff and families from the neighborhoods around the Al Aqsa hospital.

-ABC News' Zoe Magee

The Israel Defense Forces claimed on Sunday that it has "completed the dismantling of Hamas' military framework" in the northern Gaza Strip, hitting hundreds of targets and taking out key leaders of the terrorist group.

In an assessment of the first three months of the war between Israel and Hamas, Rear Adm. Daniel Hagari, an IDF spokesperson, said Israeli forces have met their goals through airstrikes, ground operations and intelligence gathering in the primary objective of eliminating Hamas.

He said the IDF's efforts in northern Gaza have included a relentless barrage of missile strikes, most of them targeting Jabaliya, the onetime stronghold of Hamas. In Jabaliya alone, Hagari said IDF airstrikes had hit 670 targets before ground forces entered the area and another 300 targets after ground troops moved in and helped direct precision airstrikes.

"In these strikes in the Jabaliya area, we eliminated the battalion commander, the deputy brigade commanders, and 11 company commanders leading the terrorists in the field," Hagari said during a news conference.

Among the Hamas commanders eliminated was Ahmad Randor, Hagari said, showing what he said was a photograph of Randor sitting with his command echelon in a bunker 40 meters, or about 131 feet, underground.

"We have completed the dismantling of Hamas' military framework in the northern Gaza Strip and will continue to deepen the achievement, strengthening the barrier and the defense components along the security fence," Hagari said.

Since the war started, IDF forces have located and destroyed 40,000 weapons across the Gaza Strip, some of which were found in schools, hospitals, mosques, and even under the beds of children, Hagari said. In Jabaliya, IDF troops also infiltrated about 5 miles of tunnels and more than 40 tunnel shafts leading to Hamas' northern headquarters and retrieved the bodies of five hostages, according to Hagari.

"Hamas no longer operates in an organized manner in this area. We have deprived it of its main terror capabilities in the region," Hagari said.

He noted that while there are still terrorists in the Jabaliya area, "they now operate without a framework and without commanders."

-ABC News' Jordana Miller

While taking questions on the tarmac in Greece before heading to Jordan in his latest round of Middle East shuttle diplomacy, Secretary of State Antony Blinken wouldn't reveal diplomatic conversations on the latest flareup in northern Israel, where Hezbollah missiles struck early Saturday, but said the U.S. is "actively working" on the issue.

"One of the areas of real concern is the border between Israel and Lebanon," he said, pointing to the "tens of thousands forced from their homes in northern Israel."

"We are looking at ways diplomatically to try to defuse that challenge, that tension, so that people can return to their homes, that they can live in peace and security," Blinken said.

Blinken said the broad priorities of his trip include "preventing this conflict from spreading," to "maximize the protection for civilians, maximize humanitarian assistance, getting it to them, and also to get hostages out of Gaza," and paving the way for a postwar, "Palestinian-led" Gaza.

He also praised U.S.-Greek cooperation, pointing to the Greeks' help in Operation Prosperity Guardian to keep the Red Sea safe amid increasing Houthi attacks on commercial vessels.

"I can't think of a time when the partnership, the friendship between our countries has been stronger," he said.

-ABC News' Chris Boccia