RNA - Lavrov also said Friday that militants belonging to the group, which has recently changed its name to Fateh al-Sham Front, were refusing to leave the besieged city of Aleppo.
Western media frequently point to the change of the name, contending that the terrorist group had distanced itself from al-Qaeda.
The US has been refusing to separate terrorists from what it describes as "moderate" militants in Syria, leading to a standoff which wrecked a ceasefire agreement with Russia last month.
Lavrov further said Moscow is very concerned by reports that Turkey is bombing northern Syria.
Turkey sent tanks and troops to northern Syria in August, storming a major city after Takfiri terrorists left without resistance. Ankara is supporting the so-called Free Syrian Army militants who are a sworn enemy of the Syrian government.
Asked what Russia thought about a Syrian government threat to shoot down Turkish warplanes violating its air space, Lavrov said Syria is a sovereign nation.
The foreign minister further said Moscow was prepared to continue a pause of bombing of east Aleppo if militants do not initiate attacks.
Terrorists continue shelling 'humanitarian corridors'
As he spoke Syria said the government has buses and ambulances ready for medical evacuations but "terrorists" were using mortars and snipers to attack humanitarian corridors and crossing points.
The Syrian ambassador in Geneva told Reuters that the government gave the UN a green light for Aleppo medical evacuations two days ago.
The UN meanwhile said the evacuations planned for Friday have been delayed after warring parties in the city failed to give necessary security assurances.
The head of the UN's humanitarian task force for Syria, Jan Egeland, said Thursday all the "green lights" needed to start medical evacuations on Friday had been given.
The UN and Red Cross had hoped to take advantage of the unilateral "humanitarian pause" in east Aleppo to evacuate the injured.
Syria’s ambassador told a UN General Assembly session on Thursday that al-Qaeda-linked terrorists were preventing civilians from leaving the areas they control in east Aleppo.
Bashar al-Ja’afari said Damascus has set up eight passageways for people to leave the city, six for civilians and eight for militants interested in government-offered amnesty or transfer to other areas.
However, the Takfiri terror outfits of Nusra Front and Ahrar al-Sham are shelling the exit routes and preventing civilians from leaving militant-held areas, he said.
UN chief's failure to mention terrorists
At the General Assembly session, Russian Ambassador Vitaly Churkin was critical of UN officials and states for failing to focus on the fight against terrorism in Syria.
Churkin strongly criticized UN Secretary General Ban Ki-moon for failing to mention the presence of terrorist organizations in Syria in his speech at the meeting devoted to the issue.
"What is happening in this room makes us really puzzled," Churkin said.
"How come that when speaking about the situation in Syria, about the toughest humanitarian situation there, the UN Secretary General makes no mention about the terrorist organizations whatsoever - neither Jebhat al-Nusra nor Daesh?" he said.
"Is tackling terrorism not one of the main goals of the United Nations?" Churkin added.
Earlier speaking at the informal meeting of the UN General Assembly, Ban welcomed the unilateral pause in Aleppo bombing. The UN chief said the conflict continued to reach "new and awful depths" with horrific results.