President Bush (search) and Russian President Vladimir Putin (search) on Thursday both agreed that neither Iran nor North Korea should have a nuclear weapon and said their respective countries have more issues in common than not.

Both leaders appeared in a joint press conference Thursday after meeting behind closed doors on issues such as the nuclear capabilities of Iran and North Korea, democracy in Russia and the War on Terror. Observers had wondered if the public appearance would be contentious, given U.S. concern over some of Putin's recent actions, which some argue are rolling back democracy in his country.

"We've had an open and candid exchange of views," Bush said. "We’ve produced a lot of positive results at this meeting."

Bush noted that he and the Russian leader have had a very cordial, friendly relationship over the past four years, adding, "that's the way I'm going to keep it for the next four years."

The two leaders also have embraced new measures to combat nuclear terrorism and better safeguard nuclear arsenals.

"We agreed to accelerate our work to protect nuclear weapons and materials both in our two nations and around the world," Bush said.

The two countries also announced an agreement designed to restrict the availability of shoulder-fired missiles that could be used to bring down aircraft.

Under the agreement, both nations would share information, take inventories of such weapons, destroy "excess and obsolete" ones, and coordinate efforts to keep them out of the hands of terrorists.

The possession of the shoulder-fired missiles (search) in the hands of criminals or terrorists pose a threat to both passenger and military aviation, a White House statement said. Approximately 1 million of these weapons have been produced worldwide, and thousands may now be in the hands of "non-state actors," the statement said.

Bush said the two discussed their differences, but stressed that countries in the 21st century will only be secure and prosperous if they have strong democracy and freedom.

Standing side by side, the two leaders' answers to questions about democratic backsliding in Russia showed the sensitivity of the topic.

"It's very important that all nations understand the great values inherent in democracy — rule of law and protection of minorities, viable political debate," Bush said. "And when I brought that — Vladimir can speak for himself on this issue. All I can tell you is he said, 'Yes meant yes when we talked about values that we share.'"

"Russia has made its choice in favor of democracy," Putin said. "This is our final choice and there is no way back, there can be no return to what we used to have."

Putin added: "We are not going to make up, to invent any kind of special Russian democracy. We are going to commit to the fundamental principles that have been established in the world."

But despite Putin's assurances, he had criticism for aspects of the U.S. system.

He suggested those who oppose his actions can buy public opinion because they "are richer than those who are in favor."

Closing out a European goodwill tour, Bush met Putin on Thursday in this snow-blanketed capital of Slovakia, once part of the Soviet bloc. It was their first meeting since Bush began his new term in January. The leaders opened talks at the medieval Bratislava Castle overlooking the snow covered capital and the Danube River. About a dozen troops, clad in fur-trimmed red and blue uniforms, stood at attention. Elsewhere in the capital, security was tight. Hundreds of heavily armed police officers and sharpshooters kept watch and helicopters flew overhead.

The 800-Pound Gorilla

Both leaders are walking a fine line, wanting to air their grievances without undercutting generally improved relations between the old Cold War nuclear rivals who are now cooperating closely in the War on Terror.

"Overall, cordiality is what the two men will seek … they want to make sure the United States and Russia have good state-to-state, cooperative relations," James Goldgeier, former director of Russian affairs for the National Security Council (search), told FOX News ahead of the Bush-Putin meeting.

"The 800-pound gorilla in this room is the rollback of democracy in Russia," added Marc Ginsberg, a former ambassador to Morocco and FOX News foreign affairs analyst, noting recent disappearances of reporters and political opponents in Russia, as well as Putin's attempts to renationalize the energy sector there.

"Putin is trying to become a person who is, in effect, trying to control the world's oil supply," Ginsberg said.

Bush seeks to balance those concerns with a desire for continued cooperation on security issues such as terrorism, weapons proliferation and energy.

"It's in my country's interest that Russia be a strong and viable partner of the United States," Bush continued. "Strong countries are built by developing strong democracies so we talked about democracy. Democracy always reflects a country's culture and customs and I know that," he added, but those democracies must abide by the rule of law, protect the free press, allow political opposition, etc. He credited Putin with overseeing an "amazing transformation of a nation."

Russian officials dislike what they see as U.S. meddling in their internal affairs and in former Soviet republics where Moscow's influence is waning. Putin argues that the Russian people are accustomed to strong rule by czars and a large government role in everyday life.

Putin has sent mixed signals — offering conciliatory talk aimed at boosting Russia's international standing and its chances for membership in the World Trade Organization (search), but at other times saying America has double standards on terrorism and is seeking to spread a dubious form of democracy.

"It's a complex relationship," Bush's national security adviser, Stephen Hadley, said of the U.S.-Russian dynamic, adding that democracy in Russia remains "a work in progress."

Thank You, Slovakia

Before his meeting with Putin, Bush met with Slovakia's president and prime minister and addressed thousands of citizens who huddled together against a wet snowfall in a town square. Bush told the people of Slovakia that they've shown that a small nation built on big ideas can spread liberty throughout the world.

He also hailed the country's triumph over communist rule in 1989 and repeatedly drew parallels between the collapse of communism and the overthrown of Saddam Hussein (search). And he thanked Slovakia for its modest contribution to the Iraq war effort.

"For the Iraqi people, this is their 1989 and they will always remember who stood with them in their quest for freedom," Bush said.

Bush said he and Prime Minister Makulas Dzurinda discussed U.S. visa restrictions, a subject of concern throughout Europe. The president assured the Slovakian leader that he was working to ease the restrictions, but cautioned "it won't happen instantly."

The two leaders also discussed the campaign to persuade Iran to abandon its nuclear weapons ambitions.

The Associated Press contributed to this report