ROME — If there were any doubt about which current European leader is closest to President Bush, Prime Minister Berlusconi of Italy erased it here yesterday.

Appearing with Mr. Bush at a press conference held in a breathtaking Renaissance villa overlooking the Eternal City, the garrulous Mr. Berlusconi called Mr. Bush a “personal friend,” a “very close friend,” and a “very unique person,” and praised his “vision” and “courage.” Mr. Berlusconi also offered to help in efforts to stop Iran from pursuing a uranium enrichment program and, Mr. Bush said, cleared the way for Italian troops in Afghanistan to operate in areas with the heaviest fighting.

Mr. Berlusconi made the unusual suggestion that Mr. Bush could be a visiting professor at a new Italian school to be called “The University of Liberal Thinking.”

Mr. Bush did not respond to that idea, but returned the kind words. “We’re good friends, and I appreciate that very much,” he said.

Mr. Bush’s visit with Mr. Berlusconi was part of his third stop on an 8-day farewell European trip, which will continue Friday morning with his third visit with Pope Benedict XVI at the Vatican. Mr. Bush met with Chancellor Merkel of Germany earlier in the week, and will also see President Sarkozy of France and Prime Minister Brown of Britain.

The Europeans in the group have been part of a notable warming in the trans-Atlantic relationship during Mr. Bush’s second term, a trend Mr. Bush is expected to cite in a speech scheduled for today in Paris.

The closer ties among leaders stand in contrast to European public opinion, which remains heavily against Mr. Bush. Scattered protesters demonstrated in Rome yesterday, including some who chanted “Bush go home!” as he arrived for a meeting with President Napolitano of Italy.

Mr. Berlusconi, the swashbuckling press baron and financier who was returned to office in May after losing power in 2006, has been one of Mr. Bush’s staunchest allies on the world stage. He was the first European leader to back the Iraq war, and has unabashedly stood by an American president who has remained consistently unpopular among the Italian public.

During yesterday’s news conference, Mr. Bush said Mr. Berlusconi had assured him that Italy had removed “caveats” that had restricted the use of Italian troops in the areas of Afghanistan with the heaviest fighting against the Taliban. Italy’s previous resistance to sending any of its 2,700 troops in Afghanistan to those areas has prompted complaints from NATO and America.

Mr. Berlusconi also repeated his offer to join a six-nation group that is conducting talks with Iran, noting Italy’s large commercial ties with that country.

Mr. Bush, however, said only that he “would seriously consider it.” Other nations in the group appear cool to the idea, and White House aides said this week that opening the door to more members could create problems.

The group, which includes Germany and the five permanent members of the U.N. Security Council, is expected in coming days to present Iran with a new offer of incentives to abandon a uranium enrichment program and open its doors to international inspectors. During an American-European Union summit earlier this week in Slovenia, leaders issued a joint statement threatening to impose banking restrictions and other sanctions if Iran does not comply.