A Syrian man walks past destroyed buildings on Monday in Aleppo's Bab al-Hadid neighborhood, which was hit by airstrikes. (Karam Al-Masri/AFP/Getty Images)

A Syrian rebel assault on government-held parts of Aleppo killed as many as 19 people, activists and Syrian state media said Tuesday, in attacks that included a deadly rocket strike on a hospital even as diplomats struggled to find ways to quell the fighting.

The United Nations special envoy for Syria, Staffan de Mistura, traveled to Moscow to push for a halt to the violence that monitoring groups say has killed more than 250 people in the past week. Russia is a key ally of Syrian President Bashar al-Assad.

“We all hope” that there will soon be “a relaunch of the cessation of hostilities,” de Mistura said at a joint news conference with Russian Foreign Minister Sergei Lavrov.

An earlier cease-fire brokered by the United States and Russia across Syria has all but collapsed.

“What the Syrians want to hear is no bombs, no rockets, no shelling, no aerial bombing," de Mistura said. Then peace efforts will be back “on the right track.”

But on Tuesday, the official Syrian Arab News Agency (SANA) said "scores" of people were killed or injured in rebel shelling of government neighborhoods in the western part of Aleppo, which has been divided between the rebels and the regime since 2012. The number of dead and injured could not immediately be confirmed.

Rebel fighters attacked several government positions in the Zahra neighborhood of Aleppo but were eventually repelled, activists said. The Syrian military also said it had fought off "terrorist" forces in the area, according to a statement reported by the Associated Press.

The bombardment included a rocket attack on a hospital and maternity clinic in Aleppo, SANA reported. At least three women were reported killed.

The strike came just hours before the U.N. Security Council passed a unanimous resolution calling for an end to attacks on health-care workers and facilities worldwide. Support for the resolution gained momentum after a deadly air raid on the Quds hospital in rebel-held Aleppo killed more than 50 people last week.

"This resolution cannot end up like so many others, including those passed on Syria over the past five years: routinely violated with impunity," Joanne Liu, international president of Doctors Without Borders, which supported the Quds hospital, said in an address to the Security Council on Tuesday.

"In Syria, where health care is systematically targeted and besieged areas are cynically denied medical care . . . uphold your obligations," Liu said.

The mounting death toll in Aleppo, Syria's largest city, has stirred international outrage and concern that the country's civil war could be tumbling into a new round of bloodshed and humanitarian misery.

Syria's information minister, Omran al-Zoubi, warned Tuesday that the government was ready to strike back against rebels shelling civilian areas. Opposition-held areas have also been pummeled by Syrian government airstrikes, and at least two people were killed Tuesday in the city’s Fardous district, activists said.

As many as 400,000 people have been killed in the five-year conflict, de Mistura said last month.

In Moscow, Lavrov said the United States and Russia would establish a joint center in Geneva to monitor the Syrian conflict. The United States has been launching airstrikes against the Islamic State in Syria and has also supported some rebel groups.

"U.S. and Russian counterparts will be sitting at the same table. They will be looking at the same maps," Lavrov said of the proposed monitoring center. "They will work together to make sure that any violations [of the cease-fire] are nipped in the bud."

“There are groups in Syria trying to escalate violence," Lavrov said. "And they shouldn't be allowed to do so."

Zakaria Zakaria in Istanbul and Brian Murphy in Washington contributed to this report.