Trump, whose aggressive use of Twitter against rivals was a key element of his presidential campaign, tweeted a list of several world leaders he had spoken with since his upset victory in the Nov. 8 presidential election.
"I have received and taken calls from many foreign leaders despite what the failing @nytimes said. Russia, U.K., China, Saudi Arabia, Japan," the Republican real estate magnate wrote in a morning Twitter post, misspelling the word "received."
"Australia, New Zealand, and more. I am always available to them. @nytimes is just upset that they looked like fools in their coverage of me," Trump continued.
He focused on the Times, a frequent Twitter target for Trump, because it said U.S. allies were "scrambling to figure out how and when to contact Mr. Trump."
"The failing @nytimes story is so totally wrong on transition," he tweeted. "It is going so smoothly. Also, I have spoken to many foreign leaders."
On Tuesday night, Trump had defended his transition team amid reports the team is in disarray, behind schedule and marked by infighting.
"Very organized process taking place as I decide on Cabinet and many other positions," Trump said on Twitter. "I am the only one who knows who the finalists are!"
Entering Trump Tower in New York on Wednesday morning, Trump's son, Eric Trump, was asked by reporters if any positions would be named on Wednesday. He responded, "Likely."
Trump tweeting about contacts with foreign leaders on such a public forum drew immediate criticism, with conservative political commentator David Frum questioning the wisdom of such posts.
"Vladimir Putin reading Trump Twitter feed this AM. 'So Merkel has not yet called him? Hmm. That’s useful to know,'" Frum said on Twitter.
"When does President Trump compromise an important secret?"
Longtime Trump supporter U.S. Representative Chris Collins, the transition team's congressional liaison, brushed off the morning Twitter storm, saying Trump was under a lot of pressure and needed to blow off steam.
"If this is his way of relaxing, God bless him," Collins told CNN. "You don't want this stuff all bottled up.
During his campaign, Trump has attacked media reports he found unfavorable to him, often targeting the Times by referring to it as "failing" while regularly granting its reporters interviews.
The Times reported on Wednesday that the presidents of Egypt and Israel got through to Trump quickly but British Prime Minister Theresa May had to wait 24 hours before reaching him.
Since his upset win over Democrat Hillary Clinton, Trump also has talked with the leaders of other countries, including Russia, China, Saudi Arabia and Australia.
He spoke last week with Japanese Prime Minister Shinzo Abe, who on Thursday will be the first foreign leader Trump meets with as president-elect.
Trump, whose aggressive use of Twitter reportedly led to calls for restraint from his inner circle, said in a CBS "60 Minutes" interview broadcast on Sunday that he would be "very restrained" on Twitter as president, if he used it at all.