"Russia together with the Syrian government have already announced the establishment of humanitarian corridors in Eastern Ghouta", Lavrov told the United Nations Human Rights Council.
"Now, it is the turn for the militants and their sponsors to act, militants entrenched there who still continue shelling Damascus, blocking aid deliveries and the evacuation of those wishing to leave", he added.

Russian Foreign Minister Sergey Lavrov delivers a speech during the 37th session of the Human Rights Council in Geneva. Source: AAP
It comes as a report in the New York Times said North Korea shipped supplies that could be used to produce chemical weapons to Syria.
Acid resistant tiles, valves and thermometers are among the items supplied by North Korea, according to a report by a panel of expert investigators who oversee compliance with UN sanctions on Pyongyang cited by the newspaper.
North Korean missile technicians were also seen working at known chemical weapons facilities in Syria, the newspaper said.
At least 40 unreported shipments of possible chemical weapons components made between 2012 and 2017 were outlined in the expert report seen by the New York Times, but the materials could be used for both military and civilian purposes.
Syria and North Korea have a warm relationship going back decades. In 2015, al-Assad's government named a park in Damascus after North Korea's founding father Kim Il Sung.
The chief spokesman for UN Secretary-General Antonio Guterres said he had not seen the report from the team of experts who are tasked with investigating sanctions violations.
But "the last thing that we need in Syria are more weapons and, god forbid, more chemical weapons," Stephane Dujarric told reporters.

People inspect the rubble of damaged buildings after several airstrikes a day earlier, rebels-held Douma, Eastern Ghouta. Source: AAP
Syria agreed to destroy its chemical weapons stockpile under international pressure following a sarin gas attack on an opposition-held area near Damascus in 2013.
But Syrian President Bashar al-Assad's government has been repeatedly accused of using chemical weapons in attacks on civilians by the UN, including in a sarin gas attack on Khan Sheikhoun in April last year.
Activists have also accused the government of carrying out chlorine gas attacks, most recently this week.

An affected child receives treatment after a gas attack on al-Shifunieh village, in Eastern Ghouta, Syria, 25 February 2018 (issued 26 February 2018). Source: AAP