WASHINGTON — President-elect Donald J. Trump met on Monday with David H. Petraeus, the highly decorated but scandal-scarred former military commander, who has emerged as a new contender for secretary of state after days of bitter internal feuding over who will get the coveted post.

Mr. Petraeus, a retired general and former C.I.A. director, spent an hour with Mr. Trump at his offices in Trump Tower in Manhattan and told reporters afterward that the president-elect had given him a tutorial on world affairs.

“He basically walked us around the world,” Mr. Petraeus said. “Showed a great grasp of a variety of the challenges that are out there and some of the opportunities as well. Very good conversation, and we’ll see where it goes from here.” In a Twitter post 15 minutes later, Mr. Trump said, “Just met with General Petraeus — was very impressed!”

Mr. Trump spent the day in back-to-back meetings after a quiet Thanksgiving weekend at his Mar-a-Lago estate in Palm Beach, Fla. In addition to seeing Mr. Petraeus, he met with Frances Fragos Townsend, a Homeland Security official in the Bush administration, and with David A. Clarke Jr., the Milwaukee County sheriff. Both are candidates for secretary of Homeland Security.