Zagreb, Croatia ? President Bush and Russian President Vladimir Putin, winding down an uneasy partnership frayed by rising tensions, sought to put relations on a stronger footing Friday with mutual assurances there will be no new Cold War.

Known to admire each other’s frankness and toughness even when they disagree, the two leaders emphasized cooperation as they began three days of farewell meetings at a gathering of NATO leaders in Bucharest, Romania. Bush referred to himself and Putin as “two old warhorses” nearing the end of their presidencies, a Bush aide said after the closed-door session.

Still, harsh differences divide Moscow and Washington, particularly on security issues.

For his part, Putin made clear he was unhappy about the eastward expansion of the Western military alliance toward Russia. But he summed up his message to Bush and NATO this way: “Let’s be friends, guys, and engage in an honest dialogue.”

It was a striking change from Russia’s once-angry threats to target missiles on Western capitals and Putin’s unrelenting drive to clamp down on democracy, expand control over the government and the economy and quash independent news media.

Finished with talks in Bucharest, Bush flew to Zagreb to celebrate NATO’s membership invitations to the Balkan countries of Croatia and Albania and an expected offer for Macedonia to join some day.

In his toast at dinner to welcome Bush, Croatian President Stipe Mesic, a staunch opponent of the war in Iraq, appeared to take a slight jab at the president by insisting that problems like terrorism, global warming and environmental destruction must be addressed jointly.

Bush, in his toast, congratulated Croatia on its NATO membership and praised it for sending troops to Afghanistan.

At a square in downtown Zagreb – far from the heavily guarded venues being used for the Bush visit – about 250 people held an anti-war protest, holding banners reading “USA NATO imperialism” and “The United States of Aggression.”

Today, Bush will go to Russia for a social dinner with Putin at the Black Sea resort of Sochi. On Sunday they will meet one last time before the Russian leader steps down on May 7. Putin’s handpicked successor, Dmitry Medvedev, will take part in some of the discussions. Putin is expected to continue to wield substantial power as Medvedev’s prime minister.

It was seven years ago in June that Bush famously declared he had looked into Putin’s soul at their first face-to-face meeting and found him to be honest, straightforward and trustworthy. Relations grew stronger when Putin stood with the United States after the Sept. 11 terrorist attacks. But the era of cooperation quickly began to unravel.