The draft resolution's proposed 10-day pause will only help militants regroup and recover strength, Lavrov said.
"Considering the way previous pauses passed, we have no doubts the 10-day pause for militants will be used by the extremists to regroup and recover strength and will therefore impede the liberation of Eastern Aleppo," the minister said.
Experts from Russia and the United States will begin their work Aleppo on Monday, the top diplomat said following talks with Philippine Foreign Affairs Secretary Perfecto Yasay, Jr. They will raise the issue of militants' withdrawal from Eastern Aleppo.
"As we announced last Saturday, December 3, the work of Russian and American experts on the problem of Eastern Aleppo is starting now in Geneva on a proposal from the United States," Lavrov said.
"During Russian-American consultations, specific routes and timeframes for militants to leave Eastern Aleppo will be agreed," he said.
The ceasefire regime in Aleppo will take effect after the routes and dates of militants' withdrawal from the Syrian city are agreed, Lavrov said.
"As soon as such routes and dates are agreed, the ceasefire regime will enter into force in order to start evacuation of those combat groups," he said.
He expressed hope that Russian-US cooperation on the issues would be fruitful, and the city would be cleared of militants.
Russia will treat militants who refuse to leave eastern Aleppo as terrorists, and will support the efforts of the Syrian government to fight them, the minister said.
"The armed groups that refuse to leave eastern Aleppo will be equated to terrorists. They will continue the armed struggle by not wanting to leave eastern Aleppo. We shall treat them as such, as terrorists, extremists. We shall continue to support the operation of the Syrian army against such gangs," he told reporters.
Washington has asked to delay Russian-US consultations on Aleppo, Lavrov said.
"We believe that Americans, when they put forward their initiative on the necessity for all militants to leave Eastern Aleppo, were aware what steps it will require from them and their allies who influence militants that settled in Eastern Aleppo," the Russian foreign minister said.
"We were ready to meet in Geneva even today, but Americans asked to postpone the consultations by a day or a day and a half, they are likely to start tomorrow evening or Wednesday morning," he said.
Previous internationally mediated ceasefires have collapsed as militants continued attacks and opposition failed to expel al-Nusra Front, which is now known as Jabhat Fatah al Sham and outlawed in Russia, from the city.