The Russian president has said he will invite Hamas leaders to Moscow for talks, following the militant group's victory in Palestinian elections.
Mr Putin said Hamas came to power "via legitimate means"
"We must respect the choice of the Palestinian people," Vladimir Putin said during his visit to Spain.
Hamas officials said they would be "delighted" to visit Russia.
The US and EU - who both classify Hamas as a terrorist group - have ruled out any dealings with the group until it renounces violence against Israel.
Russia - who together with the US, EU and UN make up the so-called Middle East Quartet - does not consider Hamas a terrorist group.
"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," Mr Putin said at a news conference in Madrid.
A spokesman for the Israeli foreign ministry said the president's remarks apparently put Russia at odds with the other members of the quartet.
The spokesman also reiterated that Israel would not negotiate with Hamas until it recognised Israel's right to exist, renounced terror and accepted the Middle East peace process.
'Looking for solutions'
"Having maintained our contacts with the organisation Hamas, we intend to invite their leaders to Moscow in the near future," Mr Putin said.
Hamas is viewed as a terrorist organisation by the US and the EU
"We have to look for solutions for the Palestinian people, for the international community, and also for Israel.
"We are deeply convinced that burning bridges is the easiest, but not a very promising activity," Mr Putin said.
The Russian special envoy to the Middle East, Alexander Kalugin, said later that Moscow would ask Hamas to recognise Israel's right to exist.
"There cannot be any dialogue without it," Mr Kalugin was quoted as saying by Russia's RIA-Novosti news agency.
In Gaza, senior Hamas official Ismail Haniyeh said the group "would be delighted" to visit Russia, according to Reuters news agency.
Over recent years, there has been an increasing gap between Russia's aspirations for influence in the Middle East, and its actual status on the ground, the BBC's Steven Eke says.
With Hamas' electoral victory in January, Mr Putin may simply have perceived an opportunity to step in - and re-assert his country's influence - while others were considering how to respond, our correspondent says.