Government forces now control the strategic area around al-Kindi Hospital in northern Aleppo, pro-regime media and activists said, strengthening their push toward the rebel-held eastern part of the city.
While the regime gained power on the ground, more airstrikes fell on rebel-held eastern Aleppo Sunday, several residents told CNN.
"Indiscriminate bombing and shelling continues in a shocking and unrelenting manner, killing and maiming civilians, subjecting them to a level of savagery that no human should have to endure," United Nations aid chief Stephen O'Brien said Sunday.
The M3 hospital was hit Sunday, a day after the city's M10 hospital was bombed for the second time in a week.
No one died in the M3 hospital attack. But with only one of Aleppo's four hospitals fully functioning, many civilians wounded in the constant assaults on Aleppo have nowhere to go.
"The health system is on the verge of total collapse, with patients being turned away," the U.N.'s O'Brien said in a statement.
He called for a 48-hour weekly pause in the fighting so aid could enter the city.
"Hundreds of critical medical evacuations are urgently required. With clean water and food in very short supply, the number of people requiring urgent medical evacuations is likely to rise dramatically in the coming days."
What does the regime say?
An estimated 10,000 Syrian-led troops have gathered in advance of a possible final ground assault by Syrian forces against rebels in Aleppo.
The past week's assault on rebel-held areas of the key city involved some of the worst violence since the start of the war in 2011.
On Sunday, the Syrian military called on rebels to leave the besieged eastern areas of Aleppo, saying that the Syrian and Russian armies "guarantee their safety," according to a statement from the Syrian Armed Forces.
The military called for "all armed men in the eastern neighborhoods of Aleppo city to leave these neighborhoods and leave the civilian residents to live their lives normally," the statement published on state-run media said.
It added that the Syrian and Russian military leaders will also "offer them necessary assistance."
How bad are the hospital attacks?
Government warplanes have targeted civilian gathering places such as markets, hospitals and mosques for several days, an activist with the opposition Aleppo Media Center told CNN.
The M10, Aleppo's largest surgical hospital, was hit Saturday for the second time in four days
. The facility was struck by
"torrent" of weapons including two barrel bombs, two cluster bombs and at least one rocket, said Adham Sahloul, spokesman for the Syrian American Medical Society.
One person died and 15 were wounded in the bombings, the Aleppo Media Center activist said.
Some patients hurt in that attack were also wounded when bombs struck the same facility Wednesday, the activist said. The M10 is now out of service, the activist said, including the desperately needed intensive care unit.
The city's M2 hospital was also put out of service by shelling Wednesday, activists said.
The Syrian American Medical Society supports both hospitals.
About 30 doctors now remain in eastern Aleppo for a population of about 300,000, Sahloul said.
Three other medical facilities in the al-Shaar neighborhood -- a women's hospital, a children's hospital and the central blood bank -- were also hit Friday, Sahloul said.
The civilian suffering doesn't end with the bombings. Most people in eastern Aleppo lack access to clean water following infrastructure damage from shelling and bombing, Sahloul said.
Why no US military intervention?
Secretary of State John Kerry, in a meeting with a group of Syrian civilians last week, expressed sympathy for their demands
that the United States intervene more forcefully amid Syrian and Russian airstrikes, according to an audio recording obtained by CNN.
He told the group that he had "lost the argument" for using military force against the regime of Syrian President Bashar al-Assad.
"I've argued for the use of force. I'm the guy who stood up and announced that we're going to attack Assad for the use of weapons," Kerry said, referring to internal deliberations within President Barack Obama's administration after Assad's use of chemical weapons in 2013.