Mr Putin issued the invitation at the end of a two-day visit to Spain in what analysts see as part of his strategy to place Russia centre stage in a year when it has assumed the chairmanship of the Group of Eight (G8) industrialised democracies.
"Maintaining our contacts with Hamas, we are ready in the near future to invite the Hamas authorities to Moscow to hold talks," Mr Putin told a news conference in the Spanish capital Madrid
Spanish Prime Minister Luis Rodriguez Zapatero backed the move, which Hamas' spokesman in Gaza, Sami Abu Zuhri, said it would happily accept as an opportunity to "explain its position and its vision regarding Israel's deceptive policies."
Ismail Haniyeh, a senior Hamas official said in Gaza that leaders of the group, whose charter calls for Israel's destruction, "would be delighted" to visit Russia if Putin tendered a formal invitation.
Russia’s move took the US by surprise with White House officials asking for details and reminding Moscow it had endorsed demands that Hamas abandon armed resistance and recognise Israel's right to exist after winning Palestinian elections last month.
"At this point we have sought some clarification from the Russians as to what exactly their intentions are, what their plans are," said State Department spokesman Sean McCormack.
He stopped short of objecting to the invitation extended by Russian
President Vladimir Putin and quickly accepted by Hamas, but said the US ambassador to Moscow had contacted the Russian foreign ministry to learn more.
Mr McCormack stressed that Russia was part of the diplomatic "quartet" that has demanded Hamas recognize Israel, give up its anti-Israeli attacks and respect agreements between the Palestinian Authority and the Jewish state.
"As a member of the quartet, we would certainly expect that Russia would deliver that same message," he said.
At odds with US
The Russian invitation is in stark contrast to Washington's view that Hamas should not be courted unless and until it renounces violence and recognises Israel, while Israeli officials have also ruled out talks until those conditions are fulfilled.
Hamas, considered a terrorist organisation by Washington, won a crushing victory over the long-dominant Fatah group in an election on January 25.
Setting US rules of engagement with Hamas, President George W
Bush said in a Reuters interview a week ago that Hamas must abandon its goal of destroying Israel and disarm.
A top US diplomat for the Middle East, David Welch, said Washington wants any government that meets Palestinians to also stress such issues, which a Quartet of Middle East mediators had determined to be conditions for dealing with Hamas.
Speaking through a Spanish interpreter, Mr Putin said: "We haven't considered Hamas a terrorist organisation. Today we must recognise that Hamas has reached power in Palestine as a result of legitimate elections and we must respect the choice of the Palestinian people."
Reacting to Mr Putin's remarks, Russia's special Middle East envoy,
Alexander Kalugin, was quoted by Itar-Tass news agency as saying
Russia hoped to bring Hamas "up to international requirements" and draw it into dialogue with Israel.
RIA news agency separately quoted Kalugin as saying: "We will insist that Hamas recognise the right of Israel to exist. Without this it would be difficult to arrange any dialogue."
Raising eyebrows
Israeli Foreign Ministry spokesman Mark Regev said in Jerusalem there should be no talks with Hamas until it recognised the Jewish state's right to exist, "renounced terror" and accepted the Middle East peace process.
Meanwhile an Israeli government source voiced surprise at Mr Putin's comments, calling them a departure from a position taken by the Quartet, to which Russia belongs along with the United States, European Union and United Nations.
"(Russia) agreed to the Quartet's statements, so people in Jerusalem are raising an eyebrow -- what's going on here?" the source said.
Russia's Foreign Ministry played down suggestions that Moscow was breaking ranks with Quartet partners, saying the talks will build on the group's agreement last month and will send Hamas a clear signal that it must take "responsible decisions".
"It needs to be stressed that our dialogue with Hamas will run along with contacts which leading regional parties, including Egypt, already have with this organisation," the ministry said in a statement.