(Adds quotes and details) By Matt Spetalnick and Oleg Shchedrov KENNEBUNKPORT, Maine, July 2 (Reuters) - Russian President Vladimir Putin made a new counter-proposal to President George W. Bush on Monday for reshaping a planned U.S. missile shield that has strained relations between their countries. After talks at the Bush family compound, Bush called Putin's offer "very innovative" and worthy of study, but insisted the anti-missile system must still be based in eastern Europe despite Russia's bitter objections. The informal, two-day summit on the rocky Maine coast was aimed at restoring the rapport the two leaders once enjoyed and easing tensions that have taken the U.S.-Russia relationship to a post-Cold War low. Bush and Putin turned from fishing trips and lobster meals to serious diplomacy on Monday but produced no breakthroughs. Afterward they did their best to project an image of harmony. "Do I trust him? Yes, I trust him," Bush said of Putin as they stood side by side in the Atlantic breeze. "There are times when we've agreed on issues and there are times when we haven't agreed on issues." With the two countries especially at odds over missile defense, Putin issued a new proposal, expanding on his surprise offer last month for joint use of Russian radar in Azerbaijan as an alternative to the U.S. plan. Washington has made clear it does not see Putin's earlier idea as a substitute but has yet to reject it for fear of appearing inflexible to already skeptical European allies. Putin raised the ante on Monday with suggestions to incorporate a radar system in southern Russia and bring more European nations into decision-making on missile defense under the umbrella of the Russia-NATO Council. "The relationship of our two countries would be raised to an entirely new level," Putin said. Putin has said he is not convinced by Washington's insistence that the anti-missile shield, with key components based in Poland and the Czech Republic, was meant to defend against "rogue states" like Iran. Moscow considers it a security threat and an impingement on its former sphere of influence. IRAN SANCTIONS? Seeking some common ground, Bush, pushing for tougher U.N. sanctions against Iran, said Putin shared U.S. concerns about Tehran's nuclear program. But it remained unclear whether Moscow, which has softened previous sanctions packages, would go along with the U.S. effort. Putin only said further discussions were needed. Aides had portrayed the talks not as a venue for major agreements but a time for the leaders to rekindle their personal chemistry. Putin is the first foreign leader Bush has hosted at the century-old Kennebunkport compound, reflecting a growing U.S. sense of urgency about reversing the slide in relations. Bush and his father, former President George H.W. Bush, took Putin on a fishing expedition on Monday morning, and the Russian president was the only one to hook a fish. Putin's aides said the two leaders had a discussion over dinner about upcoming elections in both countries that will choose their successors and agreed on the need to prevent campaign politics from impinging on U.S.-Russia relations. Bush famously said in 2001 he trusted Putin after gaining a "sense of his soul." Since then, U.S.-Russian ties have slid to the lowest level since the Cold War. Emboldened by Russia's energy wealth and his own popularity at home, Putin has adopted a more assertive posture on the world stage. At the same time, Putin seems to sense Bush's weakness. Bush's approval ratings have slipped below 30 percent in his final 19 months in office amid growing public disenchantment with the Iraq war, which Putin opposed. The two countries also disagree over Kosovo. Washington backs its independence from Serbia. Moscow opposes it. Adding to tensions has been a recent spate of harsh rhetoric, with Bush chastising Russia for backsliding on democratic reforms and Putin seeming to compare U.S. foreign policy to that of the Third Reich. (Additional reporting by Caren Bohan)
