Russia has called on Hamas to transform itself into a political organisation, recognise Israel's right to exist and keep peace accords previously agreed.
Khaled Meshaal told Sergei Lavrov he wanted to build ties with Russia
Foreign Minister Sergei Lavrov made the call during talks with leaders of the Palestinian militant group.
Hamas political leader Khaled Meshaal said the talks in Moscow had been constructive and open.
However, he again insisted that Israel must withdraw from territory occupied in 1967 if it wants peace.
Mr Lavrov said Russia would do everything possible to achieve a comprehensive peace agreement in the Middle East and that Moscow respected the democratic choice of the Palestinian people when they elected Hamas.
Break in ranks
The talks mark a break in ranks between Russia and other members of the so-called Middle East peace Quartet.
Israel has expressed anger at Russia's invitation to Hamas, with one minister calling it a "stab in the back".
The rest of the Quartet - the US, UN and EU - consider Hamas a terrorist organisation and have refused to deal with the group.
Hamas has carried out hundreds of deadly attacks against Israeli targets since the early 1990s.
Mr Lavrov told the group that in its new role it must change itself into a political party and respect the position laid down by the Quartet's negotiators.
"That means above all the need to stick by all existing agreements, the need to recognise the right of Israel to exist as a partner in negotiations, [and] the need to reject all armed methods of settling political questions," Russian news agency Interfax quoted him as saying.
"I don't think Hamas would have any serious future if Hamas doesn't change," Mr Lavrov said.
A Russian foreign ministry statement released after the talks said Hamas had said it was willing to abide by a ceasefire agreed a year ago "on the understanding that Israel will also refrain from violent actions".
Mr Meshaal said that Hamas was "interested in Russia playing a special role in the Palestinian issue" and would seek, as the new Palestinian government, to build up ties with Moscow.
He said he hoped Russia would "take a stance protecting the legitimate rights of the Palestinian people".
Ahead of the talks, Hamas leaders said the question of recognising Israel's right to exist was not up for discussion.
"The issue of recognition is a decided issue," Mr Meshaal told reporters on arrival in Moscow. "We don't intend to recognise Israel."
President Vladimir Putin invited the group to Moscow following its election victory but is not due to meet the six-member delegation.
Russia believes Hamas should not be politically isolated, but the diplomatic offensive is a controversial one that is not without risks for Mr Putin, says the BBC's Emma Simpson in Moscow.
The meeting means a great deal to Hamas because it brings international recognition, our correspondent says.
For Russia, the talks were an opportunity to become a key player in the region as well as help restore its position as a global player, our correspondent adds.