The two leaders, 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 on the shield.