The Syrian Observatory for Human Rights warned that if the ceasefire broke down, there was the risk of even greater bloodshed.
The forces of Syrian President Bashar al-Assad, backed by Russian warplanes, have been pummeling eastern Aleppo as they seek to wrest it from rebel control.
Russian Federation extended a truce in Syria's Aleppo for another 24 hours, as the United Nations said it delayed planned evacuations from the city due to security concerns.
Asked if the deployment of a Russian aircraft carrier into the eastern Mediterranean was intended as a warning for the US against striking Assad's forces, Peskov said Russia already has sufficient military assets in Syria.
But the spokesman for the U.N's humanitarian aid agency, Jens Laerke, described an "astronomically hard situation", although he declined to specify who was responsible for the breakdown in the plans on Friday.
"Medical evacuations of sick and injured could unfortunately not begin as planned because the necessary conditions were not in place", said Jens Laerke of the UN's humanitarian office OCHA.
Russian Federation is extremely dissatisfied with the way opposition groups, the United Nations and humanitarian agencies are conducting evacuations of the wounded and the sick from Syria's eastern Aleppo, a diplomatic source close to the International Syria Support Group told RIA Novosti on Friday. He spoke to reporters in Geneva.
"The terrorists are doing everything to prevent civilians and the militants from leaving eastern Aleppo", he said. "There are just two options: Assad sitting in Damascus or the Nusra sitting in Damascus", Peskov said, referring to al-Qaida's branch in Syria, which renamed itself as Fatah al-Sham Front earlier this year.
"We have taken all measures, we have buses and ambulances ready".
"These shocking acts in Aleppo beg for an appropriate investigation and those who commit them must be held accountable", he said.
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By midday Friday, no evacuations were seen along the Aleppo corridor. "There are no guarantees".
Syrian state media accused rebels of preventing people from leaving the city's opposition-held sector.
Yasser al-Youssef, a member of the political bureau of the Nour el-Din el-Zinki rebel group, said the opposition had agreed to the initiative to evacuate wounded and allow in aid, but the Syrian government and Russian Federation gave no assurances the wounded would not face arrest.
Before the pause, Aleppo's besieged districts were subjected to relentless Syrian and Russian airstrikes for weeks.
In a videotaped address, Zeid asked the U.N. Human Rights Council in Geneva to set aside its "political disagreements" and make a referral to the ICC.
The resolution called for the UN's existing Commission of Inquiry for Syria (COI) to "conduct a comprehensive, independent special inquiry into the events in Aleppo", and to identify individuals responsible for the most serious violations.
The Red Cross team was unable to enter rebel-held eastern Aleppo, under siege since July, Sedky said. He said the "collective failure of the global community to protect civilians and halt this bloodshed should haunt every one of us".
The council voted 24-7, with 16 abstentions, at a special session on the "deteriorating situation of human rights" in Syria and in Aleppo. He spoke to the AP Thursday in Paris, on the sidelines of a ministerial summit.
More than 2,000 civilians have been wounded since the regime launched its offensive to drive the rebels out of the eastern districts they have held since 2012.
All humanitarian corridors that should be used by civilians and militants to leave Aleppo are blocked by terrorists, Rudskoy said, adding that the corridors are constantly under militants' fire.