"The militaries of the two countries should determine the specific parameters of such cooperation in practice and on terrain," Lavrov told reporters in the Black Sea resort of Sochi at an international meeting on security issues, the Xinhua News Agency reported.
"We are ready to assist in such a dialogue," he added, according to video footage provided by the Russian Foreign Ministry.
In 1998, Turkey and Syria signed an agreement in the southern Turkish city of Adana, according to which Syria stopped supporting the Kurdistan Workers' Party (PKK) considered as a terrorist party by Ankara, and expelled its leader Abdullah Ocalan, which paved the way for his capture by Turkey in 1999.
On Oct. 9, Turkey started a military offensive dubbed Operation Peace Spring in the east of the Euphrates River in northern Syria to "secure its borders by eliminating terrorist elements and to ensure the safe return of Syrian refugees and Syria's territorial integrity."
Ankara claims it wants to clear east of the Euphrates River in northern Syria of the People's Protection Units (YPG), which it sees as the Syrian affiliate of the outlawed PKK, listed as a terrorist organization also by the United States and the European Union.
Lavrov said that Russia has always recognized the legitimate interests of Turkey in ensuring the security of its borders.
At the same time, Moscow is in favor of the current situation being resolved through dialogue between the Syrian government and the Kurdish structures, Lavrov said.
Such a dialogue has begun and it is yielding concrete results, he said.
The Kurdish Autonomous Administration of North and East Syria said on Sunday that it had reached an agreement with the Syrian government on the deployment of Syrian troops along the Syrian-Turkish border to aid the Kurdish-led Syrian Democratic Forces in facing the Turkish offensive and recapturing areas that had fallen to the Turkish forces.
Lavrov said Russian President Vladimir Putin and his Turkish counterpart Recep Tayyip Erdogan are planning to meet later this month.
They will discuss the situation in Syria, as well as the tasks of ensuring its sovereignty and territorial integrity "in an uncompromising struggle with the remnants of terrorist gangs and, of course, simultaneously promoting the political process in the form of organizing the first inaugural meeting of the constitutional committee," Lavrov said.