Foreign Minister Sergei Lavrov made the call during talks in Moscow with leaders of the Palestinian militant group.
Mr Lavrov told Hamas that in its new political role, it must respect the position laid down by the so-called Middle East quartet - Russia, the United States, United Nations and European Union.
“That means above all the need to stick by all existing agreements, the need to recognize the right of Israel to exist as a partner in negotiations, and the need to reject all armed methods of settling political questions,” Mr Lavrov told the group.
Hamas leader, Khaled Meshaal, said the talks had been constructive but he signaled there would be little change for now.
He reiterated Hamas’s demand for Israel to withdraw from all Palestinian territory occupied in 1967 if it wants peace.
Mr Meshaal said Israel bore the blame for the Middle East impasse and claimed it always turned away from its responsibilities.
In a statement after the talks, the Russian foreign ministry said however that Hamas vowed to stick by a ceasefire with Israel.
Hamas has carried out hundreds of deadly bombings and attacks against Israeli targets since the early 1990’s.
Tight security
The talks were the most high profile appearance yet made by Hamas on the international stage.
They were held under intense security, with eight bodyguards wearing black trenchcoats standing behind Mr Meshaal and his colleagues during the press conference.
The talks have angered Israel which expressed anger at Russia’s invitation to Hamas.
One minister reportedly called it a “stab in the back.”
The rest of the Middle East quartet have refused to deal with the group insisting that it is a terrorist organisation.