(CNN) -

Donald Trump's campaign was entirely unconventional, and his transition to 1600 Pennsylvania Ave. is proving to be just that.

But there were signs on Thursday that the weight of the presidency is beginning to sink in for Trump, and that the President-elect may be shifting from the bomb-throwing tactics he employed during the campaign to a more nuanced approach.

The President-elect held his first meeting with a world leader, Japanese Prime Minister Shinzo Abe, on Thursday. It was a most unusual setup -- arranged without any formal briefing for Trump from the State or Defense departments.

The chaotic nature of the Trump transition continues to give jitters to Democrats, some Republicans in Washington, as well as allies in governments around the world. For months, diplomats and world leaders have watched Trump deliver incendiary speeches on the campaign trail with wariness and trepidation.

But Abe spoke positively about the meeting afterwards, calling it a candid conversation and saying he believed they could form a relationship of mutual respect.

Trump also arranged meetings with Republicans who were among his fiercest critics, a display of normalcy after a week of upheaval and apparent chaos for his transition team.

First, he replaced New Jersey Gov. Chris Christie, who had been overseeing the transition, with Vice President-elect Mike Pence, and subsequently purged lobbyists from the ranks, in keeping with his vow to "drain the swamp" in Washington.

Then there was the lightning rod announcement of former Breitbart chief executive Steve Bannon as a top White House adviser -- which sent shockwaves through activist groups who view the Breitbart site as racist and anti-Semitic.

Thursday, more conventional Republican faces began appearing at Trump Tower as the team continued vetting potential Cabinet members and advisers at a furious pace, with literally thousands of government positions to fill within a very short window of time.

Trump met with foreign policy heavyweight Henry Kissinger, as well as Alabama Sen. Jeff Sessions and one-time critic South Carolina Gov. Nikki Haley, who are both under serious consideration for Cabinet jobs.

In perhaps the most surprising news, Trump plans to meet this weekend in New Jersey with 2012 Republican nominee Mitt Romney, who was one of Trump's most vociferous critics during the campaign (calling him a phony, and a fraud, and skewering him on Twitter for the way in which he talked about women on a leaked "Access Hollywood" tape).

Romney may be considered for a Cabinet post -- possibly secretary of state -- though sources close to the former Massachusetts governor say he has not actively sought a role in the Trump administration and merely agreed to meet with Trump as a gesture of good faith.

Establishment Republicans viewed the more recent developments with relief on Thursday -- a signal that Trump may be giving more serious thought to addressing the deep fissures in his party.

Trump's outreach to Haley and Romney, seemed to demonstrate a possible willingness to assemble a team of rivals in his government -- which would be a surprising pivot for a man who wrote in his 1997 book "The Art of the Comeback" that one of his maxims was to "get even" and that he believed "in an eye for an eye.

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Many world leaders were eager to make contact with him after his surprising victory last week. But with Trump's own team in transition, that was no easy feat.

For example, Trump was connected with the Australian prime minister, sources told CNN, by a mutual acquaintance, golfer Greg Norman, who happened to have his phone number.

Several diplomats told CNN that they reached out to Trump Tower to schedule congratulatory calls for their head of state. . Once the calls were arranged, they were connected without being asked for any verification of their identities or measures to verify the authenticity of the call.

Some diplomats who had set up meetings with transition team members for the coming days discovered those officials were gone as part of this past week's purge of Christie's team and anyone registered as a lobbyist.

Amidst the initial confusion about who was in charge, one diplomat wondered whether to reach out directly to Trump's son-in-law Jared Kushner, who is one of his closest advisers, or his daughter Ivanka Trump.

Having been elected without any prior government experience, Trump's conversations unsurprisingly are bucking traditional diplomatic protocol The Times of London reported on a leaked transcript of Trump's call with British Prime Minister Theresa May, where Trump reportedly offered her the most casual of invitations to meet with him: "If you travel to the US, you should let me know."

'A certain amount of chaos'

After Trump's White House meeting with President Barack Obama, there also was a lapse in communication with the current agency personnel who will ensure a smooth transition of power.

That problem -- delays created by Trump's team not getting paperwork and a list of names to the White House -- appeared to be corrected Thursday when a transition official reported that four teams -- from the Department of State, Department of Justice, Department of Defense and National Security Council -- have been connected with the proper agency points of contact.

While Trump's team has come under a hail of criticism this week, both Democratic and Republican officials who have been involved in past transition planning cautioned that a fair amount of chaos was to be expected, particularly given that many of Trump's own advisers did not expect him to win. Presidents-elect generally don't announce major nominees like Secretary of State within nine days of the election anyway.