A U.S. Border Patrol agent was shot and killed on Monday afternoon on Interstate 91 in northern Vermont, about 12 miles from the Canadian border.

The shooting, in which another person was also killed and a third was wounded, was being investigated by the Albany office of the F.B.I. as an assault on a federal officer, the agency said in a statement.

The wounded person was taken into custody, the statement said, but the F.B.I. did not immediately announce charges and provided no additional details.

Officials said the shooting occurred about 3:15 p.m. in the town of Coventry. Interstate 91 was initially shut down in both directions, though the northbound lanes later reopened. The southbound lanes were expected to remain closed for “a long duration closure,” the Vermont State Police said in a news release.

The F.B.I. said in its statement that it needed time to “gather evidence and process the scene,” adding: “While there is no threat to the public, Interstate 91 will remain closed due to investigative activity.”

Agents on the Northern border have seen a growing number of attempted illegal crossings in recent years, making more than 23,000 arrests during the fiscal year that ended in September, according to U.S. Customs and Border Protection. That number is more than twice that of the previous year.

Most of the arrests were made in the Swanton Sector, a vast rural stretch of border roughly 300 miles long between Quebec, New York and northern New England, which includes Vermont. The agent killed on Monday was assigned to the Swanton Sector, officials said.

Vermont’s lawmakers in Washington expressed condolences for the border agent’s family in a joint statement, and urged greater support for the patrol on the Northern border. “Together, we must do everything possible to prevent future tragedies like what happened today,” said Senator Bernie Sanders, an independent, and Senator Peter Welch and Representative Becca Balint, both Democrats.

Canadian officials have attributed much of the increase in border arrests to immigrants from India who arrive in Canada on temporary visas and then cross the border into the United States.

Border officials have also seen an increase in encounters with migrants from Mexico who fly to Canada and cross into the United States. Most show up at ports of entry to request asylum, but others try to enter the country illegally.

Despite the increase, the number of attempted illegal crossings from Canada remains much smaller than the number occurring at the Southern border with Mexico.