Casualties in a Syrian government assault on the rebel stronghold to the east of Damascus are thought to include as many as 100 children, with several hospitals reported to have been hit.
At Prime Minister's Questions, SNP Westminster leader Ian Blackford asked Theresa May to step up calls for existing UN resolutions on ending the siege of civilian areas to be enforced.
Mrs May said she was "appalled by the escalation of air strikes in Eastern Ghouta and deeply concerned by reports of the ongoing deliberate targeting of civilians and civilian infrastructure, in blatant violation of international humanitarian and human rights law."
"There is concern that something like 700 people who need medical evacuation are being refused that evacuation by the regime. We will continue to work with the UN and the UN Geneva-led process. The UN envoy has our full support for his work to try to bring an end to this by finding a political solution for Syria."
Mr Blackford called on the Prime Minister to "show leadership" and support his demand for an urgent meeting of the UN Security Council to tackle what he said was a "horrific genocide" unfolding in Syria.
"The bombing is relentless," Mr Blackford said. "Doctors on the ground are treating pregnant women and babies who have lost limbs. It is estimated that well over 100 children have been killed since Sunday. The UN has issued desperate pleas calling for political intervention."
The Prime Minister replied: "We will talk to our UN colleagues to ensure that the best possible approach can be taken in relation to these issues, but it is not just about the Syrian Government; it is about the backers of the Syrian Government as well.
"We call on all their backers, including Russia, to ensure that the violence stops, and that those people who are need of help are given that help."
Mr Blackford was among SNP parliamentarians who voted against joining US air strikes on Bashar al-Assad's regime in 2015. Asked after PMQs whether he had changed his mind on military action, Mr Blackford said he was still opposed to bombing, and said humanitarian and diplomatic efforts should be the priority.