Vladimir Putin, the president of Russia, extended the invitation to Hamas last week, after its sweeping victory in Palestinian elections last month.
Hamas, which remains committed to Israel's destruction and has been branded a terrorist organisation in the US and Europe, is to form a new Palestinian government in the coming weeks.
Sami Abu Zuhri, a Hamas spokesman in Gaza, said Russia and Hamas would engage in a dialogue during the group's visit.
"We are going to present our positions ... about the political developments and issues related to the rights of our people," Abu Zuhri said on Saturday.
"Russia will listen to Hamas and Hamas will listen to Russia."
Although an official date for the visit has not been set, Abu Zuhri said he expects it to take place this month.
Putin's position runs counter to the stand recently taken by the so-called Quartet of Mideast peace negotiators, comprising Russia, the US, the European Union and the
The Quartet, which backs the "road map" peace plan, has called on Hamas to renounce violence and recognise Israel.
"We are going to present our positions ... about the political developments and issues related to the rights of our people"
Sami Abu Zuhri, a Hamas spokesman in Gaza
It has also threatened to withhold hundreds of millions of dollars in aid to the Palestinian Authority once Hamas takes power.
The invitation, later supported wholeheartedly by France, infuriated Israel, which fears that the international resolve to shun the group is weakening.
On Sunday, Tzipi Livni, Israel's foreign minister, urged other countries to stand firm against Hamas, which has killed hundreds of Israelis in suicide bombings.
"The Russian position is currently not accepted in the international community," Livni told Israel Radio.
"Part of the danger is going down the slippery slope of first talking, then starting to understand why, then supporting with money, then granting legitimacy. This is a phenomenon that needs to be acted against."
With Hamas issuing mixed messages about the future of its military activities, Livni cautioned the world against accepting vague Hamas statements.
"There is no negotiation here with Hamas about what it will and will not agree to," she said.
"The conditions here are very clear, the situation is black and white."
"The Russian position is currently not accepted in the international community"
Tzipi Livni, Israel's foreign minister
Hamas, while adhering to its violent ideology, has voiced willingness to agree to a long-term truce if Israel would reciprocate. Hamas has largely honoured a year-old ceasefire.
The Israeli defence ministry said on Sunday that Sergei Ivanov, the Russian defence minister, had invited his Israeli counterpart, Shaul Mofaz, to visit Russia to make Israel's views known, but Mofaz had not decided whether to accept the invitation.
The two men met on Saturday on the sidelines of a Nato meeting.
Frank-Walter Steinmeier, the foreign minister of Germany, is due to arrive in Israel on Sunday for talks on relations between Israel and the Palestinians after Hamas's election victory.