Hamas leader Khaled Meshaal is in Moscow for talks aimed at lobbying Russia to push for an end to a Western aid embargo on the Palestinian government.
"Our goal is to encourage the international community to start co-operation with the Palestinian government and pressurise Israel to recognise the Palestinian state's right to exist," he was reported as saying.
"We value Russia's position towards lifting the blockade from which the Palestinian people suffer. We also value Russia's special position in the issues of the Middle East settlement."
Russia has taken a softer line on the Islamist Hamas than the United States and the European Union, which along with the United Nations make up the Quartet of Middle East peace negotiators.
"The Quartet should radically review its stance and send its demands to Israel, rather than to the Palestinians," Meshaal said.
The West is boycotting Hamas and the government it formed after an election victory last year, demanding it recognises Israel, renounces violence and accepts interim peace deals.
Moscow is the last leg of Meshaal's tour, which included Egypt and Iran.