LONDON - There was no peering into anyone's soul, and there was no bonding over Colgate toothpaste.

But U.S. President Barack Obama, while taking a more businesslike approach to diplomacy than his predecessor George W. Bush, used his debut on the world stage to start developing his own brand of rapport with fellow world leaders.

In Obama's first face-to-face meeting with Russian President Dmitry Medvedev, there were smiles and handshakes but none of the backslapping that characterized the relationship between their predecessors, George W. Bush and Vladimir Putin.

Aides said it was a conscious effort by the U.S. president, known for his no-drama Obama style, to strike up a more formal relationship with his Russian counterpart when they met on the sidelines of a G20 economic crisis summit in London.

Our strategy is to develop an agenda based on interests, also accentuating where we disagree, but not to make the goal of these meetings to establish some buddy-buddy relationship, one U.S. official said after the talks.

It was a stark contrast to Bush, who said after his first meeting with Putin in 2001 that had gotten a sense of his soul. Critics later said Bush had been naive to trust the former KGB spymaster.

Russian Foreign Minister Sergei Lavrov detected a new approach and welcomed it.

The new atmosphere of mutual trust, an atmosphere which does not create the illusion of good relations because they develop well on a personal level but which ensure taking into account mutual interests and readiness to listen to each other, we missed this much in recent years, Lavrov told reporters.

There are reasons to believe that this time it will not end only in good personal relations.

Despite the personal chemistry between them, Bush and Putin -- who went fishing together in Maine and danced to Russian ballads on the Black Sea -- presided over a period in which U.S.-Russia relations sank to a post-Cold War low.

Obama and Medvedev tried on Wednesday to push the restart button on ties between Moscow and Washington.

In the process, the closest the two came to finding a connection was Medvedev's observation -- as they sat in matching chairs with a flower vase between them -- that as former lawyers they had a common language.

BARACK AND GORDON

Obama and Prime Minister Gordon Brown also had to tackle a litany of policy challenges but they managed a lighter mood than when the British leader visited the White House last month and British media described his treatment as second-rate.

At a joint news conference, they called each other Barack and Gordon but fell short of the chumminess between Bush and former British Prime Minister Tony Blair, whose fall from power was partly blamed on his closeness to the unpopular Bush.

Though normally eschewing Bush's folksiness, Obama gushed over his and first lady Michelle Obama's impending audience with Queen Elizabeth at Buckingham Palace.

Brown also said the two leaders had bonded over exercise treadmills and the ups and downs of domestic politics.

I've benefited from Barack's advice not just about elections, but about fitness, Brown said, marveling over Obama's exercise discipline, even when on the road.

Obama, riding high in public approval ratings at home and wildly popular overseas, also offered encouragement to Brown, down in opinion polls, on electioneering, telling him to continue showing integrity.

Adding a personal touch, Obama mentioned he had taken time in between discussions of Afghanistan and Iran to talk to Brown's two young sons about dinosaurs.

It was a far cry, however, from Bush's first meeting with Blair when the president said he had discovered the two had at least one thing in common -- both brushed with Colgate.

Serious diplomacy prevailed again in Obama's meeting with Chinese President Hu Jintao. Though the body language was much like the Medvedev session, it was Hu who reached out to Obama, saying he wanted to establish a personal friendship.

(Additional reporting by Oleg Shchedrov, editing by Mike Peacock)