WASHINGTON — President-elect Donald Trump is expanding his pool of candidates for secretary of state, leaving unclear whether former CIA Director David Petraeus' guilty plea for leaking classified information disqualifies him to serve as the nation's top diplomat.

“There's not a finite list of candidates” for secretary of state, top Trump adviser Kellyanne Conway told reporters Sunday. “More than four. Who knows how many finalists there will be?”

Trump is also continuing to defend his engagement with the leader of Taiwan, a breach of diplomatic protocol as the U.S. shifted recognition from Taiwan to China nearly 40 years ago. In a series of evening tweets on Sunday night, Trump groused about criticism that he didn't work with China ahead of the Friday contact. China considers Taiwan a rogue province.

Regarding the list of candidates for secretary of state, Conway's remark comes a week after Trump's aides confirmed that the president-elect had settled on four finalists for the post. Two people close to the transition said that Trump is moving away from two of the four: former New York City Mayor Rudy Giuliani and Mitt Romney, the 2012 Republican presidential nominee.

That would leave Petraeus as a top contender, along with Tennessee Republican Sen. Bob Corker, chairman of the Senate Foreign Relations Committee. Both people close to the transition said Trump's prolonged decision-making process has left the door open to other options. Among other possibilities, one official says, is Jon Huntsman, a former Republican Utah governor who also served as the ambassador to China under President Barack Obama and speaks Mandarin.

The people close to the transition spoke on condition of anonymity because they were not authorized to discuss the private process publicly.

There was other evidence that Trump is looking beyond the known four contenders. Vice President-elect Mike Pence on Sunday listed the quartet, but added a fresh reference to former U.N. ambassador “John Bolton or others who may be added to the list” of candidates.

It seemed unclear Sunday even to Petraeus and Trump's inner circle whether the retired general's guilty plea has turned off Trump.

Petraeus, a retired four-star general, pleaded guilty last year to one misdemeanor charge of mishandling classified information relating to documents he had provided to a woman he was having a sexual relationship with. He was spared prison time under a plea agreement with the Justice Department and was given two years' probation.

FBI Director James Comey has drawn a distinction between Petraeus' case and that of Democratic presidential nominee Hillary Clinton's use of a private email server while she was secretary of state by saying there was no evidence that Clinton or her aides had intended to break the law through careless handling of sensitive information. Federal prosecutors said Petraeus knew black binders he shared contained classified information, but he nonetheless provided them.

“I made a mistake. I have again acknowledged it,” Petraeus said Sunday on ABC's “This Week.” “Folks will have to factor that in and determine whether that is indeed disqualifying or not.”

Regarding China and Taiwan, Trump tweeted late Sunday: “Did China ask us if it was OK to carry out a number of actions such as build up disputed islands in the South China Sea or take economic measures hurtful to the United States,” Trump tweeted.

The Taiwanese leader, Tsai Ing-Wen, called Trump Friday to congratulate him on the election in a call set up by an American third party.