NOVO OGARYOVO, Russia (Reuters) - U.S. President Barack Obama praised Prime Minister Vladimir Putin’s achievements Tuesday, attempting to mend fences with Russia’s powerful politician after criticizing him for Cold War thinking.

Obama went out of his way on the second day of his visit to compliment Putin, a former KGB spy who is the dominant partner in a power “tandem” with current President Dmitry Medvedev.

The U.S. leader said he had a good two-hour meeting with the former Kremlin chief at Putin’s forest residence outside Moscow, where officials said the two men had a frank breakfast talk.

“I am aware of not only the extraordinary work that you’ve done on behalf of the Russian people in your previous role as prime minis-, uh, as president, but in your current role as prime minister,” Obama said at the start of talks.

“We think there’s an excellent opportunity to put U.S.-Russian relations on a much stronger footing,” he said.

Putin, looking visibly awkward, told Obama that U.S.-Russian relations had a mixed history, sometimes flourishing but with grey days and even some confrontations.

The former KGB spy then invited Obama for a black caviar breakfast -- complete with a Russian samovar, smoked beluga, pancakes and tea -- on the terrace of his residence.

The 56-year-old Putin is known for setting great store on personal relationships with world leaders, though his warm ties with George W. Bush coincided with a stormy diplomatic links between the two countries.

COLD WAR WARRIOR?

Obama ruffled feathers in Moscow ahead of his visit by saying that Putin needed to “understand that the Cold War approach to U.S.-Russian relationship is outdated” and that Putin had “one foot in the old ways of doing business.”

Putin rejected the remarks but the criticism -- rare in Russia -- was interpreted by local media as an attempt to test the Kremlin tandem.

“An attempt by the U.S. president to split the tandem hits Medvedev as much as Putin,” popular commentator Mikhail Rostovsky wrote in Moskovsky Komsomolets daily.

“Does the Russian president need the reputation of a leader whose main ally in a domestic power play is the Americans?”

“Ex-Soviet president (Mikhail) Gorbachev can testify that there cannot be a more harmful stamp for a politician in this country.”

Obama, who dispensed with much of the ceremony usually rolled out for visiting leaders, constantly praised the 43-year-old Medvedev during the two days of Moscow talks.

“My strong impression is, is that President Medvedev and Prime Minister Putin are working very effectively together,” Obama said later.

“I had a good conversation with the prime minister and I think his approach to the issues is very similar to yours,” Obama later told Medvedev.

A senior U.S. official speaking to reporters on condition his name was not used said Obama had been convinced Putin was “a man of today and has got his eyes firmly on the future.”

Commenting on the official’s words, Putin spokesman Dmitry Peskov said: “If that is not a result then what is?”

“The conversation was very good natured and substantial, we had many common points in many areas,” Putin was quoted as telling reporters after the meeting.

Putin’s chief of staff Yuri Ushakov said the two leaders spoke about Georgia and Ukraine, which have been sparring points in bilateral ties over the past year.

“They spoke about Georgia, they spoke about Ukraine and generally about the post-Soviet area. The U.S. President promised to take into account the peculiarities of our (relations) with these countries,” he was quoted as saying by Interfax news agency.