Hospital officials said Israeli forces had fired on the facilities and that snipers had been deployed near one of them.
"Today marks the third day of the siege on Al-Awda Hospital in northern Gaza," the hospital's acting director Dr Mohammad Saleh told AFP.
He reported that Israeli forces had been "firing at the hospital buildings" and that "snipers" have taken up position in nearby houses.
Dr Saleh said the "southern wall" of the hospital "has been destroyed" and "all medical staff and patients" are inside the hospital wards.
Moving around the hospital was "extremely difficult", he said.
But staff still had to transfer water "from the second building to the first one because the occupation (Israeli) forces hit the first building with a shell on the fifth floor yesterday (Monday), destroying the water tanks".
WHO chief Tedros Adhanom Ghebreyesus said at a press conference in Geneva that "148 hospital staff, 22 patients and their companions are trapped inside" the hospital.
The WHO regularly visited Al-Awda in April to deliver medical supplies and fuel, but Ghebreyesus also reported snipers aiming at the building and artillery hitting the fifth floor.
Evacuation under way
Dounia Dekhili, emergency coordinator for Doctors Without Borders (MSF) in Gaza, said "nothing is coming in or out" of the hospital because of fears of sniper fire.
"Our operating theatre supervisor has been hiding for a few days, he can hear gunshots," Dekhili told AFP after speaking to the man inside Al-Awda.
Dr Saleh did not report any casualties, but said the episode was reminiscent of the last Israeli military operation in the area of the northern Gaza hospital, which is located next to the Jabalia refugee camp.
In December, Israeli forces besieged Al-Awda for days, killing two staff and detaining others, MSF reported at the time.
Despite AFP requests, the Israeli military has yet to comment on the operation in Al-Awda.
Tuesday also saw patients and staff being evacuated from another north Gaza hospital, Kamal Adwan, its director Dr Hossam Abu Safia told AFP.
"Currently, the hospital is being evacuated of the wounded, patients, and medical staff," he said, adding that "there are several patients that the medical teams have not been able to evacuate".
He said "the reception and emergency entrance gate of Kamal Adwan Hospital was targeted by an artillery shell from the Israeli army", as soldiers advanced towards the complex.
'ICU area hit'
Rik Peeperkorn, WHO representative in the Palestinian Territories, said Tuesday from Jerusalem that the hospital's intensive care unit reception area had been hit.
"At the moment, 20 health staff and 13 patients remain," Peeperkorn said, adding that "these are ... functional hospitals we cannot afford to lose", referring to both Kamal Adwan and Al-Awda.
"These are the only two functional hospitals remaining in northern Gaza. Ensuring their ability to deliver health services is imperative," Ghebreyesus said in Geneva.
Israeli troops have previously raided other medical facilities in Gaza, including Al-Shifa in Gaza City, the territory's largest hospital, now reduced to rubble after a March operation, the WHO said.
The Gaza Strip has been gripped by war since Hamas's unprecedented October 7 attack on Israel resulted in the deaths of more than 1,170 people, most of them civilians, according to an AFP tally of Israeli official figures.
Israel's retaliatory offensive has killed at least 35,647 people in Gaza, most of them civilians, according to the Hamas-run Palestinian territory's health ministry.
