Mayor Bloomberg promoted his immigration reform ideas during a trip to Ireland yesterday, telling a group at Sligo’s City Hall that America needs to significantly increase the number of visas it issues and allow undocumented immigrants already in the country to stay.

“I know that many Irish-born New Yorkers are caught in the trap of our federal immigration policies,” the mayor said. “If we are going to attract the best and the brightest — and Ireland has more than its fair share — we need to inject some common sense into our immigration laws, and I’m doing my best to make that case in Washington.”

The one-day trip was planned so that Mr. Bloomberg could dedicate a monument in Ballymote to New York’s Fighting 69th, the famed National Guard unit with Irish roots.

The trip also put Mr. Bloomberg on an international stage and led to more questions about his presidential ambitions.

In talking up Ireland’s culture and praising the growth in its economy, Mr. Bloomberg was not only appealing to those on hand, but to Irish-Americans, an important voting bloc.

He cracked jokes about New York City’s many Irish-American officials — including his police commissioner, Raymond Kelly, and the City Council speaker, Christine Quinn — quoted the poet William Buster Yeats, and recalled all the Friday nights he spent at O’Flanagan’s Pub on the Upper East Side as young man.

Mr. Bloomberg told reporters he was flattered by the presidential speculation, but repeated his public stance that he plans to serve out his term in City Hall and become a philanthropist.

“I don’t know how many times I can say I’m not running for president, but I’ll say it one more time, I have no plans to run for president,” he said.

Nonetheless, he took on the role of dignitary yesterday. He was praised by those who organized the event and faced protests from a group of about a dozen people for his support of Israel’s attacks against Hezbollah in southern Lebanon.

Mr. Bloomberg, who as mayor has no say on foreign policy, was peppered with questions about international issues like the Iraq war and the peace talks in Northern Ireland. Although in the past his position on Iraq has been murky, yesterday he said that while nobody is in favor of war, “we have to go in and fight terrorism wherever it is.”

He also again defended Senator Lieberman, saying that putting party loyalty ahead of all else is a “disgrace.” He said the Democrat of Connecticut would have won his primary election if it had been held two days later, because the tide was turning in his favor.

In unveiling the copper cylinder-shaped memorial, which includes some metal from the World Trade Center, Mr. Bloomberg praised the bravery and service of the Fighting 69th. He was traveling with the widow of a city firefighter who was killed in Iraq and the father of a firefighter killed on September 11, 2001.

As part of the ceremony, he had an American bald eagle land on his hand and posed for photos with the 15-pound bird. The bird’s owner, Lothar Muschketat, said the eagle took well to the mayor.

“It’s not often that you get the chance to hold your nation’s national emblem on your hand,” Mr. Muschketat said. “I don’t think even the president has gotten the chance to do that.”

The bird was brought to the ceremony from Mr. Muschketat’s nearby nature preserve and research center to symbolize the union between the Irish attendees and the American delegation. The 2000 census counted about 42,000 Irish-born residents in the five boroughs.

The event organizer, John Perry, called Mr. Bloomberg an “extraordinary man for the Irish” and said, “He’s the most relaxed politician that I’ve ever met. ” He said Mr. Bloomberg went into town after the event and bought an Irish sweater.