David Petraeus, former CIA Director, is seen inside the elevator after entering the lobby of the Trump Tower in New York, NY, on November 28, 2016. [Photo/IC]

WASHINGTON - US President-elect Donald Trump on Monday met with former CIA Director David Petraeus as he ratcheted up efforts to search for a new US secretary of state.

Speaking to reporters after their one-hour meeting, Petraeus indicated to reporters that he was impressed by Trump's knowledge about international affairs.

"He (Trump) basically walked us around the world. 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," said Petraeus.

Meanwhile, Trump said on Twitter that he was "very impressed" after his meeting with Petraeus.

According to local media report, Petraeus, together with 2012 Republican presidential nominee Mitt Romney and former New York Mayor Rudolph Giuliani, are strong competitors for the position of US secretary of state in the upcoming Trump administration.