Toyako, Japan ? President Bush today called new Russian President Dmitry Medvedev a “smart guy” who understands the issues. But the U.S. president would not go so far as to say he got a sense of Medvedev’s soul, as he once famously said of Vladimir Putin after their first meeting.

“I’m not going to sit here and psychoanalyze the guy,” Bush said after his first sit-down with Medvedev since the Russian president took office. “He’s comfortable and competent, and I believe when he tells me something, he means it.”

The two leaders met on the sidelines of the Group of Eight summit. They both emphasized that there were issues of agreement between their countries- such as dealing with North Korea and Iran – but also areas of disagreement, such as U.S. plans for a European-based missile shield.

“I found him to be a smart guy who understands issues very well,” Bush said.

Medvedev, who referred to Bush informally as “George,” said Bush’s presidency isn’t over and that he intends to intensify discussions with him. The new Russian leader said he would build upon U.S.-Russia relations with the next U.S. president, whomever that turns out to be.

Medvedev took office last month as Putin’s hand-picked successor. Putin still wields enormous influence at home as prime minister.

Medvedev’s appearance could help him make the case he is emerging from Putin’s shadow and carving out a leadership role. In an interview with journalists from G-8 countries last week, Medvedev suggested that he, not Putin, is in charge.

Republican presidential candidate John McCain has urged stripping Russia of its G-8 membership because of autocratic steps by Putin. Neither fellow Republican Bush nor Democratic presidential contender Barack Obama shares that view.

Ahead of the Bush-Medvedev meeting, the Kremlin issued a statement suggesting that good personal ties are developing between Bush and the new president and that a transition period following the change of presidents in Russia “was practically unneeded.”