BELFAST, Northern Ireland — President Biden hailed 25 years of relative peace in Northern Ireland in a speech at a Belfast university on Wednesday, urging political leaders to embrace economic possibilities and turn away from violence.

After arriving late Tuesday night in Air Force One, Mr. Biden’s midday speech began a three-day mix of diplomacy and personal genealogy as he meets with political leaders and traces his own family roots.

“No matter what divides us, if we look hard enough, there are always areas that are going to bring us together,” Mr. Biden told a small audience at Ulster University in Belfast. “Standing for peace, rejecting political violence must be one of those things.”

The brief stop in Belfast on Wednesday, which included a short meeting with Rishi Sunak, the British prime minister, is expected to be followed by a series of sentimental stops for Mr. Biden in the hometowns of his Irish ancestors.

Mr. Biden will visit County Louth, the longtime home of the Finnegans, and County Mayo, the home of the Blewitts. In between, he will meet with the president and prime minister of Ireland and will deliver remarks to the Irish Parliament.

The most personal moment for Mr. Biden is expected to be a speech he delivers Friday night, just before returning to the United States. White House officials said that he would use the remarks to connect his own family story to the immigrant story for many Americans.

Wednesday

Mr. Biden touring Carlingford Castle in County Louth, Ireland.

Mr. Biden speaking to children after arriving at Dublin International Airport.

Speaking about the 25th anniversary of the Good Friday Agreement at Ulster University in Belfast.

Mr. Biden meeting with the British prime minister, Rishi Sunak, in Belfast.

Mr. Biden at Ulster University.

Crowds outside the Grand Central Hotel in Belfast as Mr. Biden met with Mr. Sunak.

Tuesday

Mr. Biden disembarking from Air Force One after arriving at R.A.F. Aldergrove, an air base near Belfast.