Eric Garcetti, still weighing a presidential run, delivers commencement address in New Hampshire

Los Angeles Mayor Eric Garcetti delivered a commencement speech in New Hampshire on Sunday, adding another notch to his travels in key primary states as he contemplates a run for president.

Garcetti flew east Saturday, speaking to graduates at Southern New Hampshire University the next morning before returning to Los Angeles, where he faces a homelessness crisis and a decision on who will be the city’s next police chief.

This was Garcetti’s second trip to New Hampshire. In August, before publicly acknowledging that he was considering a presidential run, he stumped for Manchester mayoral candidate Joyce Craig.

In recent months, Garcetti has stepped up his presence in early primary states, visiting Nevada, South Carolina and Iowa. Last week, he addressed a labor union convention in Florida.

In his Mother’s Day speech to about 1,800 graduates of SNHU’s College of Online and Continuing Education, Garcetti spoke about navigating borders both physical and psychological.

Many of the graduates had returned to school after years or decades, determined to get their college degrees amid the challenges of working and parenting. They came to the ceremony from as far away as Texas and Hawaii.

There was a contingent in the crowd from Los Angeles — “Don’t forget to vote,” Garcetti quipped. The online division has so many students from Southern California that a graduation ceremony will be held there soon, said university spokeswoman Lauren Keane.

“To get here today, each one of you had to navigate borders — borders of geography, of opportunity, borders of identity and of your own doubt,” said Garcetti, 47.

He spoke of his own grandfather, who crossed the border from Mexico as a baby, and his great-grandparents, who fled anti-Semitism in Russia.

“I’m an average American. As I joke, I’m the average Mexican American Jewish Italian mayor of the most diverse city in the world,” he said.

The theme of borders extended to national politics. Garcetti urged the audience to talk to people with opposing political views. He referenced veterans, refugees and homelessness while criticizing Washington politicians for failing to bridge differences.

“The pundits call it right now in our country that there are two Americas – there’s the rural and urban divide, the immigrant and native-born, the coasts and the heartland, red and blue,” Garcetti said. “I do believe there are two Americas, but it’s none of those – it’s Washington, D.C., and the rest of us.”

In Iowa last month, Garcetti made the standard Democratic candidate rounds — a training center for carpenters, a gay rights gala — without formally declaring that he was running.

Garcetti’s New Hampshire trip had less to do with a possible presidential run than with speaking at a school known for providing opportunities for veterans and older students, said Yusef Robb, a political advisor.

The mayor made no other official stops on the trip, Robb said.

Craig, who won her bid for Manchester mayor, introduced Garcetti to SNHU President Paul LeBlanc, Robb said, and the trip was paid for by the university.

Garcetti spoke to SNHU trustees at their recent board retreat in Los Angeles, which led to the commencement invitation, said Keane, the university spokeswoman.

In case anyone had forgotten that presidential politics were in the mix, LeBlanc slipped in a joke as he took the microphone back from Garcetti.

“Thank you, President Garcetti — uh, Mayor Garcetti,” he said.

cindy.chang@latimes.com