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The leaders signed a declaration which expressed their readiness to search for a compromise on the missile shield. Bush also had talks with Putin's protege Medvedev on whom he said he got positive first impressions.
Bush and Putin, nearing the end of their presidencies, signed a declaration which expressed their readiness to search for a compromise on the missile shield, an issue that has helped drive ties between their countries to a post-Cold War low.
Putin restated his firm opposition to the U.S. plans and the leaders wrapped up their two-day summit in the Black Sea resort of Sochi by acknowledging more work was needed to bridge their differences on the issue.
"I want to be understood correctly. Strategically, no change happened in our ... attitude to U.S. plans," Putin told reporters at a joint news briefing with Bush. "At the same time there are some positive developments. Our concerns were finally heard by the U.S. side," Putin said. "I am cautiously optimistic that we will reach an agreement."
Standing alongside each other after a morning of talks, Putin and Bush, who have built a warm personal rapport despite severe strains between their countries, paid warm tributes to each other at what will be their last meeting as heads of state.
Earlier, Bush had talks with Putin's protege Dmitry Medvedev, who will take over as Russian president on May 7. "He seemed like a straight-forward fellow, he seemed like someone who would tell me what's on his mind," Bush said. "My first impressions are very positive, a smart fellow."
The only agreement signed in Sochi was a declaration on the "strategic framework" of U.S.-Russian relations, aimed at encapsulating the legacy they will bequeath to their successors. The document noted areas where the United States and Russia are already cooperating, including trade, nuclear non-proliferation and counter-terrorism, but also mapped out ways to narrow differences, including the missile shield issue.
The summit opened on a positive note after Bush's arrival at Putin's seaside retreat on Saturday as the two joined in a Russian folk dance during an informal dinner of red caviar and veal loin. But once the night's festive mood has worn off, the leaders still face a long list of grievances.
The thorniest issue is Bush's plan for a U.S. missile shield based in eastern Europe, a system Washington says is needed to protect against Iran but Moscow says threatens its security.
HEART-TO-HEART
Bush, who leaves office in January, met the Russian leader seven years after saying he had peered into Putin's soul and trusted him. At the time, critics had universally mocked Bush as na?ve.
Since then, disputes over Kosovo, missile defense and Russia's human rights records have led to talk of a Cold War-style atmosphere developing between the two nations.
Bush had said he expected his last heads-of-state meeting with Putin, they have met more than 20 times before, to be another "heart-to-heart."
Showing their rapport was still intact, the two leaders shared a hug as Bush arrived at Putin's compound and exchanged jokes as they were briefed on plans for the 2014 Winter Olympic Games in Sochi, Putin's pet project.
Bush is out to salvage a foreign policy record dominated by the Iraq war, which has damaged U.S. credibility. He is also struggling to stay relevant on the world stage now that his economic stewardship is under fire and attention is focused on whoever will succeed him in the White House.
For his part, Putin is looking for a smooth transition of the presidency to Medvedev, elected in a landslide last month after the Russian leader endorsed him.