Donald Trump is looking for a running mate who can be a “fighter skilled in hand-to-hand combat” to help him parry criticism on the campaign trail, and he has narrowed his list to a handful of seasoned politicians.

Mr. Trump, in a telephone interview Tuesday, said his top picks include Indiana Gov. Mike Pence, former House Speaker Newt Gingrich, New Jersey Gov. Chris Christie and a couple politicians who haven’t gotten as much attention, including Alabama Sen. Jeff Sessions.

The New York businessman has said he wanted a seasoned government leader as a running mate. But in the interview, on the way to events with Mr. Pence in Indiana, Mr. Trump added a new criterion: He wants an attack dog.

“I’m getting attacked from all sides,” he said.