President-elect Donald Trump stepped up his search on Monday for a new U.S. secretary of state, with the focus on David Petraeus, a former U.S. military commander in Iraq whose mishandling of classified information led to his resignation as CIA chief in 2012.

"Just met with General Petraeus--was very impressed!" Trump said on Twitter shortly after Petraeus, a retired general, left an hour-long meeting with the Republican winner of the Nov. 8 election at Trump Tower in Manhattan.

Trump's consideration of Petraeus, who has also been mentioned as a contender for the top job at the Pentagon - adds a new layer of drama to his unusually public deliberations over the top diplomatic job for his administration.

Petraeus, who led international forces in both Iraq and Afghanistan, was sentenced to two years' probation and fined $100,000 last year for the unauthorized removal and retention of classified information.

He admitted sharing classified information with his biographer, with whom he was having an affair. The scandal forced Petraeus to resign from the CIA in 2012.

Petraeus said after meeting Trump that the New York businessman "basically walked us around the world" in their discussion. "He showed a great grasp of the variety of challenges that are out there and some of the opportunities as well," Petraeus told reporters.

Trump, who takes office on Jan. 20, plans to hold talks with Mitt Romney on Tuesday in his second recent meeting with the 2012 Republican presidential nominee.

A Republican source close to the transition team said it had appeared late last week that Trump was leaning toward choosing Romney as his secretary of state but that the appearance of Petraeus at Trump Tower suggested the president-elect was still undecided and casting a wider net for the position.

U.S. Senator Bob Corker of Tennessee, the chairman of the Senate Foreign Relations Committee, and former New York Mayor Rudy Giuliani are also in the mix for the job of America's top diplomat, Trump aides say.

Frances Townsend, a national security aide during the administration of Republican President George W. Bush, also met Trump on Monday.

PETRAEUS TROUBLES

Petraeus' past mishandling of classified documents is unlikely to be an obstacle to Trump offering him...read more at Reuters