New York Gov. Andrew Cuomo Associated Press

New York Gov. Andrew Cuomo may travel to the Dominican Republic and Puerto Rico as soon as next weekend, building on a recent flurry of overseas travel as he runs for re-election next month.

“We are considering it,” Mr. Cuomo said on Saturday, while speaking to reporters aboard a bus to a campaign event on Long Island.

The governor said he would make the excursion to “go down and pay respects.”

“The community here very much resonates with their homeland and I have a history with Puerto Rico—I did a lot of work when I was in the federal government—and Dominican Republic, too,” he said. “So if I can get it done, I would like to get it done.” Mr. Cuomo served as Secretary of Housing and Urban Development under President Bill Clinton.

The trip would come as Mr. Cuomo, after nearly four years of rarely leaving New York, has made international travel a common feature late in his first term in office.

In August, the Democrat traveled to Israel to show solidarity with that country’s fight with Hamas, touring an underground tunnel and visiting the Western Wall and the Church of the Holy Sepulchre.

In September, Mr. Cuomo and three other governors traveled on a U.S. Department of Defense-sponsored trip to Afghanistan to visit troops and receive counterterrorism briefings.

And on Tuesday, Mr. Cuomo said he planned five international trade missions to advance New York as a place to do business, including trips to China, Mexico, Canada, Israel and Italy.

Write to Erica Orden at erica.orden@wsj.com