SOCHI, RUSSIA — President Bush and President Putin of Russia failed yesterday to overcome their greatest conflicts on a missile defense system America plans to build in Central Europe but narrowed the difference over one key element.

The two presidents presented divergent assessments after spending nearly five hours together this weekend, with Mr. Bush expressing optimism that Russia was relaxing its opposition to the missile shield and Mr. Putin presenting a clear view of his objections and the obstacles in its way. “It is a significant breakthrough,” Mr. Bush said, focusing on Russia’s willingness to work on the missile shield in a partnership with America and its European allies.

“It’s not going to happen immediately,” Mr. Bush said, adding: “But is this a good opportunity to work together? You bet it is.”

But Russia continued to object to the central architecture of the system, which calls for installing radar in the Czech Republic linked to missile interceptors based in Poland. The Russians favor the use of an existing Russian radar in Azerbaijan.

Mr. Putin, focusing on Mr. Bush’s insistence on pursuing the American arrangement, said of a joint declaration they issued enumerating progress the two countries: “It does not provide any breakthrough solutions on a number of issues.”

Their difference about the weapon, Mr. Putin said, “is not about language; this is not about diplomatic phrasing or wording. This is about the substance of the issue.” “I’d like to be very clear on this,” he said. “Our fundamental attitude to the American plans has not changed.”

Mr. Bush argues that the weapon system is needed to defend against missiles launched from Iran or elsewhere in the Middle East.

The two spoke at a joint news conference held in a presidential vacation home in this Black Sea resort, where palm trees hug the shoreline and corniches, and snowcapped mountains hover just beyond the city.

With Mr. Putin stepping down May 7, the summit was almost certainly the final encounter between the two men as heads of state. It was the 22nd time they had met, apart from encounters at major international gatherings.

Mr. Putin’s successor, Dmitry Medvedev, joined them at dinner and met separately with Mr. Bush. He has said he would name Mr. Putin as his prime minister.

Mr. Bush did not use Mr. Medvedev’s name, over which many non-Russian speakers have stumbled, when talking in the news conference about him.

He said of the president-elect: “He seemed like a straight-forward fellow, somebody who could tell you what’s on his mind.”

“My first impressions are very positive — smart fellow,” Mr. Bush added.