NEW YORK - Donald Trump denied Wednesday that his White House transition is in disarray amid reports of a backstabbing purge of mainstream Republican aspirants as he puts together his new administration.

In a burst of tweets, Trump also rejected as "false" a New York Times report that foreign leaders were having trouble getting through to the billionaire president-elect.

"Very organized process taking place as I decide on Cabinet and many other positions. I am the only one who knows who the finalists are," he wrote late Tuesday.

Following up Wednesday, he rejected reports of disarray and infighting for plum posts, as "so totally wrong." "It is going so smoothly," he said. "Also, I have spoken to many foreign leaders," he said, adding in another tweet that he had taken calls from Russia, Britain, China, Saudi Arabia and Japan."

The New York Times said Trump was improvising in his conversations with foreign leaders, who in turn were scrambling to figure out how and when to contact the president-elect.

British Prime Minister Theresa May reached Trump 24 hours after Egypt and Israel, in what the Times called "a striking break from diplomatic practice."

One leader who got through was Ukrainian president Petro Poroshenko, who asked Trump on Tuesday for support against "Russian aggression" during a congratulatory call, the Ukrainian presidency said.

Separately, in an interview that aired Tuesday, Syrian President Bashar al-Assad said Trump would be a "natural ally" if he fulfills his pledge to fight "terrorists."

Meanwhile, the Democratic mayor of New York, Bill de Blasio, said he met Wednesday with President-elect Donald Trump and warned him that he would work to protect undocumented immigrants from deportation.

"I reiterated to him that this city and so many cities around the country will do all we can to protect our residents and to make sure that families are not torn apart," de Blasio told reporters after the meeting at Trump Tower.

Despite Trump's denial, there were mounting signs of turmoil in the process of selecting a Cabinet and filling an estimated 4,000 positions in the new administration.

Two members of the transition team quit, reportedly pushed out by Trump son-in-law Jared Kushner in what was described as a purge of associates of New Jersey Governor Chris Christie.

Christie was bumped Friday as chairman of the transition team.

The two were Mike Rogers, a former chairman of the House Intelligence Committee, and Matthew Freedman, a lobbyist.

As a US attorney, Christie prosecuted Kushner's real estate developer father in 2004, sending him to jail for two years.

The shakeup came amid jockeying for key posts, including secretary of state, the treasury, attorney general, defense and national security.

Several US news outlets have reported that former New York mayor Rudy Giuliani is tipped for secretary of state.

Hawkish former UN ambassador John Bolton and retired general Michael Flynn reportedly are also among those shortlisted for top administration jobs.

Vice president-elect and transition leader Mike Pence spent much of Tuesday at Trump Tower - the real estate mogul's headquarters - but his only comment to media as he left was "Great day."

Other sightings at the opulent Manhattan skyscraper included Ted Cruz - the arch-conservative Texas senator who Trump belittled as "Lyin' Ted" during the Republican primaries.

Media said Trump has requested top-secret clearance for Kushner - a real estate developer who is married to Ivanka Trump - so that he can join the daily presidential briefings.

"I am not trying to get 'top level security clearance' for my children. This was a typically false news story," Trump wrote Wednesday.

Ensconced in his Trump Tower headquarters since his shock election victory a week ago, Trump finally left the building late Tuesday to have dinner with his family at Manhattan's 21 Club.

But he left without his press pool, prompting The White House Correspondent's Association to complain that it was "unacceptable for the next president of the United States to travel without a regular pool to record his movements and inform the public about his whereabouts."

A top Trump aide has told reporters that Giuliani - a member of Trump's inner circle - is a "serious" contender to become the next secretary of state.

The crime-fighting former prosecutor was mayor of New York on 9/11, and his leadership after the World Trade Center's twin towers were toppled in the September 2001 attacks made him a hero.

But CNN reported that 72-year-old businessman's professional ties - including work as a lobbyist for a Venezuelan oil firm - could complicate his confirmation in the role.

Trump also drew fierce criticism when he also announced that anti-establishment firebrand Steve Bannon would be his chief strategist.

Bannon is the onetime head of the Breitbart website, seen by critics as a haven for white supremacists.

Bolton, a neo-conservative hawk and former undersecretary of state, also was reported to be in the running for the top diplomatic post.

He was a controversial choice for UN envoy in 2005, having once said if the UN headquarters lost 10 floors, "it wouldn't make a bit of difference." Bolton however strongly supported the Iraq war, which Trump has said he opposed.