KENNEBUNKPORT, Maine — Russian President Vladimir Putin gave President Bush more alternatives Monday for reshaping a missile defense system fiercely opposed by Moscow. Bush said the United States still wants to anchor the missile shield in Poland and the Czech Republic.

It was unclear whether the United States considered Putin's ideas acceptable.

The two leaders, meeting at the oceanfront compound of Bush's father, sought to restart U.S.-Russian relations after months of acrimony.

"Do I trust him?" Bush said of Putin, standing alongside the Russian leader on the craggy Atlantic shoreline. "Yes, I trust him."

"There are times when we've agreed on issues and there are times when we haven't agreed on issues."

Last month, Putin surprised Bush in Germany by proposing a Soviet-era early warning radar in Azerbaijan as a substitute for the radar and interceptors the United States wants to place in Poland and the Czech Republic. Washington has been clear it doubts the Azerbaijan facility is up to becoming a substitute.

The Russian leader added new suggestions Monday.

Putin proposed incorporating a radar system in southern Russia and bringing more European nations into the decision-making process about how the shield is structured. He suggested information-sharing centers in Moscow and possibly Brussels as a way to strengthen the Washington-Moscow national security relationship.

"The relationship of our two countries would be raised to an entirely new level," Putin said.

Bush called the Russian leader's latest missile defense idea "very sincere" and "very innovative."

However, the president said, "I think the Czech Republic and Poland need to be an integral part of the system."

Stephen Hadley, Bush's national security adviser, acknowledged that the two leaders do not have completely "harmonious" views about missile defense. But he said Putin's idea showed the Russian leader was serious about cooperating on the issue. Hadley cited Putin's idea to upgrade Azerbaijan station, setting up information-exchange centers and using the NATO-Russia Council as a forum for involving interested European nations in the discussion.

Both leaders smiled and seemed eager to portray a strong, stable relationship between the two nations. Putin is the first head of state to be hosted at the Maine summer home by President Bush, an attempt to warm relations in a place of sparkling views and summertime weather.

Bush said that while Putin sometimes says things he doesn't like to hear, he is convinced that Putin is telling the truth.