His comments come after Turkish President Recep Tayyip Erdogan reportedly discussed the situation in Aleppo with his Russian counterpart, Vladimir Putin, by phone for the third time in a week.
Turkish Foreign Minister Mevlut Cavusoglu met Wednesday with Riad Hijab, head of the opposition High Negotiations Committee, with the two discussing "efforts to stop the fighting immediately and to deliver humanitarian aid as soon as possible" to Aleppo, diplomatic sources said.
On November 29, Erdoğan said the Turkish military had launched its operations that started in late August in Syria to end the rule of al-Assad, despite having previously said he would "clear the Turkish border of terrorist organizations".
Russian Federation has backed Assad throughout Syria's civil war.
Both presidents also reportedly emphasized the importance of normalizing ties between them, ties which were badly strained over a year ago when Turkey shot down a Russian bomber over its border with Syria.
Speaking at a joint press conference after a meeting with his Turkish counterpart Mevlut Cavusoglu in the Mediterranean town of Alanya, Lavrov said Russian Federation would continue efforts to allow humanitarian aid into Aleppo, according to a Turkish translation of his comments. "We are there to end the rule of the cruel Assad, who has been spreading state terror".
Kremlin spokesman Dmitry Peskov told journalists he hoped that "clarification will come shortly from our Turkish partners".
IS claimed via its news agency that its militants had captured two Turkish soldiers in al-Dana village near al-Bab in northern Syria.
Ankara and Brussels agreed on a deal in March, under which Turkey pledged to take back all undocumented migrants who arrive in the European Union through its territory in exchange for Syrian refugees accommodated in Turkey, on a one-for-one basis. Should they succeed, it would be the rebels' biggest setback of the war.
"We have coordination aimed at avoiding unintentional incidents with the US-led coalition, and Turkey is part of it", Lavrov noted.