US Secretary of State John Kerry threatened Wednesday to end US engagement with Russia on Syria, further escalating tensions with Moscow over its involvement in the war-ravaged country.

The top US diplomat demanded Russia take "immediate steps" to end a military campaign on the rebel-held section of Aleppo in northern Syria that has so far killed more than 300 people.

Kerry told Russian Foreign Minister Sergei Lavrov that the US holds Russia responsible for the situation in Aleppo amid attacks on civilians by the Syrian regime, according to spokesman John Kirby.

Kerry's stance came as two out of the eight remaining hospitals in eastern Aleppo besieged by government forces were put out of action by shelling and airstrikes on Wednesday, the Syrian medical charity running them has said.

The United States is working on steps it might have to take "to begin to suspend our engagement on Syria," Kirby said without providing details about what it might do beyond withdrawing a negotiating team from Geneva.

A top leader in the Syrian National Coalition meanwhile said "a political solution is no longer a viable option in the current climate."

Muwaffaq Nyrabiya, vice president of the opposition umbrella group, said rebel groups "will be considering all options to defend the Syrian people against the Russian aggression on Syria," according to a statement on the organization's website.

The Russian Foreign Ministry said in a statement that Lavrov and Kerry talked on the phone on Wednesday, discussing ways to improve the situation in Aleppo.

Lavrov expressed concern over media reports that the UN-designated terrorist group al-Nusra Front had acquired American weaponry, and accused so-called moderate opposition groups backed by the US of violating the recent ceasefire and supporting al-Nusra Front, the statement said.

The underground hospitals - codenamed M2 and M10 - included two of the rebel-held area's five trauma and emergency care facilities, Adham Sahloul, an official with the Syrian American Medical Society (SAMS), told dpa.

"The people of eastern Aleppo have one wish now - to die immediately, and not get wounded and die from bleeding on a hospital floor," said Abu al-Izz, a SAMS doctor.

Analysts and human rights groups have previously accused President Bashar al-Assad's government and its ally, Russia, of deliberately targeting medical facilities.

"M10 was the largest facility. It has lost its ventilator and electricity generator in the shelling," Sahloul said. "By this you have sentenced people to death," he warned.

UN Secretary General Ban Ki-moon condemned attacks on the two hospitals, calling them a war crime.

"Let us be clear: those using ever more destructive weapons know exactly what they are doing," Ban said. "Imagine a slaughterhouse. This is worse. Even a slaughterhouse is more humane."

Ban also called on the UN Security Council to overcome their divisions and protect hospitals and healthcare professionals in armed conflicts.

France is proposing talks at the United Nations to obtain a ceasefire for Aleppo, said French Foreign Minister Jean-Marc Ayrault, warning that those who do not support it risk being complicit in war crimes.

Speaking to the lower house of parliament, Ayrault said Aleppo cannot become the Guernica of the 21st century, referring to the bombing of the Basque town during the Spanish Civil War in 1937.

"The brutality of the attacks that have taken place these past days and the systematic bombardment of Aleppo, the targeting of hospitals and humanitarian convoys raise the indignation of the international community," Ayrault said.

Airstrikes by the Syrian government and Russia have killed more than 298 people in eastern Aleppo, including 54 children, since September 19, when a ceasefire brokered by the US and Russia collapsed, the Syrian Observatory for Human Rights, a monitoring group, said.

At least 96 children have been killed and 223 injured in the escalating fighting in eastern Aleppo since Friday, the United Nations Children's Fund said.

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