Earlier, regime forces engaged in clashes with rebels in the eastern area of the enclave, the Syrian Observatory for Human Rights said, after advances in recent days that saw the regime seize control of 10% of the region.
The Syrian government has retaken control of more than a quarter of the rebel-held enclave of Eastern Ghouta on the outskirts of the capital Damascus, a monitoring group said.
According to the latest reports, 674 individuals are killed and another 400,000 civilians trapped in the rebel-held suburb of Damascus are in danger of losing their lives due to continuous of bombardment by Syrian armed forces with the support of Russian warplanes.
May's office said the two agreed that "Russia and others with influence over the Syrian regime must act now to cease their campaign of violence and to protect civilians".
Damascus and Moscow have accused rebels of preventing civilians from leaving.
The attacks carried out by the Assad regime and its supporters in Eastern Ghouta have killed more than 700 civilians according to reports.
He was referring to a daily humanitarian ceasefire called by Russian Federation from 9am to 2pm local time, which the United States has dismissed as "a joke".
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One resident estimated that thousands of people were on the move and seeking shelter in areas further from the frontlines.
A humanitarian convoy carrying life-saving supplies from United Nations and other aid agencies will not enter the besieged Syrian enclave of eastern Ghouta as planned on Sunday, a United Nations official in Syria told Reuters.
The main rebel units actively holding territory in Eastern Ghouta are the Islamist Jaish al-Islam and Faylaq al Rahman, which have taken part in peace negotiations in the past. "This collective punishment of civilians is simply unacceptable", he added.
The death toll in the region may rise as the attacks are still ongoing.
At least 76 pro-regime fighters and 43 rebels from Jaish al-Islam have also been killed in clashes since February 25, it says.
The Observatory said Turkish forces had advanced to within 12 km (7 miles) of Afrin. Turkish forces have taken control of the roads from Rajo and Jandaris to Afrin, it also said in a statement. A reporter from the Syrian state-run Al Ekhbariya TV, accompanying troops, broadcast from Nashabiyah, a village on the south-eastern edge of eastern Ghouta.