They will discuss relations between Syria and Lebanon ahead of the Syrian president's visit next week.
Upon his arrival, Siniora said Russia could be an influential mediator: "Syria contributed to the withdrawal of the Israeli force of occupation from Lebanese territories.
Güncelleme Tarihi: 20 Eylül 2018, 18:16
"We are grateful for that assistance... Relations between Lebanon and Syria do have a future. We are still to discuss many issues, and both countries will only benefit from this.
"I believe that Russia can exert certain efforts in this situation.
"Syria and Lebanon are two brotherly countries. Nobody will set Lebanon against Syria and nobody will govern Lebanon from Syria."
Opposition groups, led by Hezbollah, have been holding a mostly peaceful demonstration in central Beirut since December 1 calling for Siniora to resign.
In an interview given to the British business newspaper, The Financial Times, before he left for Russia, Siniora said the protests had "no future" and "would not lead to anything".
Hezbollah, which is backed by Iran and Syria, has mobilised thousands of protesters and has threatened to escalate its protests if demands for a unity government are not met.
"Escalate to where?" Siniora asked.
"They know the dangers, there are red lines in Lebanon... A takeover of the state is not achievable."
Supporters of the Free Patriotic Movement (FPM) and the Amal Christian party have joined the Hezbollah protests in what is seen as an unlikely alliance.
Alain Aoun, an FPM official, said: "Hezbollah is respecting Lebanese cultural diversity and distancing itself from the spectre of an Islamic republic along Iranian lines."
Nada Ashkar, a 28-year-old Christian, said she is not fooled by this association: "All this just for the presidency."
Ashkar pointed to what she called "social differences" that could put paid to such an alliance. "During the 2005 protests [after al-Hariri's assassination] we all slept under the same canvas - Christians, Sunnis and Druze, men and women.
"This time, however, the Hezbollah tents and those of Aoun's [Amal party] supporters are well separated from each other - by up to several hundred metres in places."