A Muslim student from Bangladesh, Nazmus Sakib Choudhury, 25, said he was afraid of a Trump presidency and intended to vote Democratic. “We don’t have an option,” he said.

Not everybody agreed. An older man from Canada, who did not want to give his name, said he wanted to use his citizenship to vote for Mr. Trump.

Maria Ester Lopez, 34, a Bronx resident from Mexico, said she felt both lucky and blessed to get her citizenship on the last day to register to vote by mail.

“It’s kind of a miracle,” she said. “Just in time.”

But not everybody made it.

In line with a national trend, applications for citizenship rose over the last 12 months in the area that includes New York City and Long Island, with 110,895 people trying to become citizens, compared with 88,627 over the previous 12-month period, according to the federal Citizenship and Immigration Services. And applicants faced significant waits. As of June 30, 72,595 applications were pending. (By comparison, 52,953 applications were pending at the same point the previous year.)

The federal Citizenship and Immigration Services, which processes the applications, denied that those numbers represented delays. “We are monitoring the situation and managing resources to address disparities in processing times,” Katie Tichacek, a spokeswoman for the agency, said.

But the Northern Manhattan Coalition for Immigrant Rights, which helped prepare 600 applications for citizenship over the last year, has noticed a substantial lag time in processing in 2016, which has resulted in some people not being naturalized in time to vote, Angela Fernandez, the group’s executive director, said. It took only three months to process applications in New York at this time last year, but now took longer than five months, she said.