Retired General David Petraeus entered the running to become secretary of state under President-elect Donald Trump, after the two held talks on Monday.

Exiting Trump Tower in New York City, Petraeus said he and Trump spoke for an hour. He praised the President-elect for showing a "great grasp of a variety of the challenges that are out there."

"Very good conversation and we'll see where it goes from here," Petraeus said. He did not respond to questions asking whether Trump had offered him a position in his administration.

Petraeus led international forces in the US-led interventions in Iraq and Afghanistan. After retiring as general, he served as CIA director in 2011-12 but was forced to resign after sharing highly classified information with his biographer, with whom he was having an affair.

The scandal tarnished the four-star general's reputation. However, a source close to the transition team said this was unlikely to be obstacle to Trump offering him a government post.

Trump tweeted shortly after the meeting: "Just met with General Petraeus-was very impressed!"

A source advising the transition team on national security told news agency Reuters that: "Just based on his public statements, I think [Trump] sees Petraeus as a good man who made a mistake, who did a fraction of what other people have done and received a lot more punishment."

Romney, Corker and Giuliani also in contention

Trump is scheduled to hold talks with a number of other contenders for the top diplomat position in the coming days. On Tuesday, he is set to meet with Tennessee Sen. Bob Corker and 2012 Republican presidential nominee Mitt Romney.

Vice President-elect Mike Pence is believed to be favoring Romney for the secretary of state position, despite him being fiercely critical of Trump during the presidential campaign. He and Trump had already discussed a potential cabinet position during a lengthy meeting earlier this month.

A source close to the transition team said that it appeared Trump had settled on appointing Romney for the top diplomat post. However, Petraeus' appearance at Trump Tower suggests the president-elect is still undecided on the position. Trump's campaign manager Kellyanne Conway is believed to have warned Trump that appointing Romney would spark backlash among his supporters.

Wrangling over the secretary of state post appears to have slowed announcements on other appointments in Trump's cabinet. Earlier reports suggested that retired General James Mattis was reportedly at the top of Trump's list for the defense secretary, while former New York Mayor Rudy Giuliani was tipped as the favored candidate to be homeland security secretary. Giuliani is also in the running for secretly of state role, although questions concerning his overseas business dealings appear to have given Trump pause.

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

As he exited Trump Tower on Monday, Pence, who is spearheading the transition process, teased "a number of very important announcements tomorrow."

Fresh investigation into Petraeus' affair

Petraeus' appearance at Trump Tower coincided with news that the Defense Department was conducting a new leaks investigation into the extramarital affair that led to the former general's resignation as CIA Director.

A US official said that the investigation concerned leaked information about Paula Broadwell, the woman with whom Patraeus had an affair and leaked information to, and the status of her security clearance at the time.

Last year, Petraeus eventually pleaded guilty to felony charges of mishandling classified information he had provided to Broadwell. He was spared a prison sentence under a plea deal with the Justice Department.

During the presidential campaign, Trump repeatedly lambasted Democratic nominee Hillary Clinton over a federal investigation into her use of a private email server while serving as secretary of state. He suggested that her actions were graver than Petraeus,' although prosecutors accuse the retired general of being fully aware the documents he shared Broadwell contained classified information. The FBI, meanwhile, has said it has found no evidence that Clinton or her aides intended to break the law.

dm/rc (Reuters, AP, AFP)