Members of the Palestinian militant group Hamas have called their visit to Moscow an "important breakthrough" amid US attempts to isolate the group.
Mr Meshaal (left) of Hamas met Russian religious leaders
One delegate, Mohammed Nazzal, said the US was trying to put Hamas under "political siege" following its victory in the Palestinian election last month.
He said the group looked forward to "good relations" with Russia.
The delegation has met religious and political leaders on the second day of its trip.
"We consider this visit to be a very important breakthrough," Mr Nazzal told the AFP news agency.
"The US administration is trying to isolate Hamas, they are trying to place Hamas under political siege.
On Saturday, the delegation, headed by political leader Khaled Meshaal, met Russian Muslim leaders, led by Mufti Sheikh Ravil Gainutdin.
The two groups shared tea together and joined each other in prayers at Moscow's main mosque, the Itar-Tass news agency reports.
Speaking after the meeting, Mr Meshaal said constructive views had been exchanged and he was pleased by the "Russians' readiness to have open relations with the Islamic world".
The team also met the chairman of the foreign relations committee of the Russian upper house, Mikhail Marguelov.
Mr Marguelov later said Hamas "will be pragmatic in its dealings with Israel", as it had been "in building a peaceful operation in Palestinian territories".
Russia is the only one of the four Middle East peace mediators to talk to Hamas since its election victory.
Russia has broken with other mediators in talking to Hamas
The rest of the Quartet - the US, UN and EU - consider Hamas a terrorist organisation and have refused to deal with the group.
Arab League foreign ministers have meanwhile agreed a draft resolution urging foreign governments against imposing what they term as "unjust" conditions on the incoming Hamas administration.
The draft, which will be debated at a summit in Sudan this month, said the world should respect the will of the Palestinians, who voted Hamas into office.
On Saturday, former Russian premier Yevgeny Primakov called Hamas' January poll victory a "complete fiasco" for US diplomacy in the Middle East.
Mr Primakov said the US was wrong to treat Hamas as a terrorist group in the wake of their political victory and should not cut off funds to the Palestinians.
During his talks with the delegation on Friday, Foreign Minister Sergei Lavrov urged Hamas to transform into a political group.
"I don't think Hamas would have any serious future if Hamas doesn't change," Mr Lavrov said.
Mr Meshaal said the talks were constructive and open.
But he insisted that Israel must withdraw from territory occupied in 1967 if it wants peace.