Western observers consider Russia's role in Egypt, Libya and Syria as a challenge to NATO, which tried to overthrow leaders in all three Mediterranean states.
According to Saif al-Islam Gaddaf's lawyer, the man once tipped to rule Libya is free.
Russia is interested in a prompt return to order in Libya, Putin's spokesman said.
But other rebels say they won't be so welcoming to the new regime.
Witnesses say some of the casualties were civilians.
Libyan Court Sentences Muammar Gaddafi's Son, Saif al-Islam Saif, and Eight Other Ex-Officials to Death
Defendants had been accused of a range of offenses including the use of deadly force against unarmed demonstrators, as well as corruption.
The children were killed on Tuesday when a rocket hit their neighborhood, near an area where army forces and Islamist brigades have been fighting
Libya wants to be able to defend itself from the encroaching terrorist threat.
Human Rights Watch outlined the dangers faced by Libya's media in a new report.
The army reportedly has retaken nearly all of Benghazi from the extremist group Ansar al-Sharia.