Here are a few highlights from the two calls, which took place on Jan. 27 and Jan. 28.
Trump urges Pena Nieto to stop publicly saying Mexico won't pay for the wall
During his phone call with Pena Nieto, Trump urged his Mexican counterpart to stop saying that Mexico will not pay for a wall on the southwestern U.S. border. A signature Trump promise during the presidential campaign was that he would build the wall and make Mexico pay for it.
"You have a very big mark on our back, Mr. President, regarding who pays for the wall," Pena Nieto said. "My position has been and will continue to be very firm saying that Mexico cannot pay for that wall."
Trump responded, "But you cannot say that to the press. The press is going to go with that, and I cannot live with that. You cannot say that to the press, because I cannot negotiate under those circumstances."
He went on, "But the fact is we are both in a little bit of a political bind, because I have to have Mexico pay for the wall. I have to."
He suggested that they publicly say they're still determining who will pay for the wall.
Trump then threatened, "If you are going to say that Mexico is not going to pay for the wall, then I do not want to meet with you guys anymore, because I cannot live with that."
Trump bashes US refugees resettlement deal with Australia: 'This is a stupid deal'
Trump's conversation with Prime Minister Turnbull turned heated when the two began discussing a refugee resettlement agreement negotiated during the Obama administration.
"I am asking you as a very good friend," Turnbull said to Trump. "This is a big deal. It is really, really important to us that we maintain it."
Trump, who on Jan. 27 signed an executive order suspending the United States' refugee program, said the deal "is going to kill me" and agreeing to it would make him look like a "weak and ineffective leader."
"This is a stupid deal," Trump declared.
He then boasted, "I am the world's greatest person that does not want to let people into the country."
Trump argued that Democrats lost the 2016 presidential election because of "stupid deals like this."
"You can certainly say that it was not a deal that you would have done, but you are going to stick with it," Turnbull said.
Trump finally conceded, "I am going to say that I have no choice but to honor my predecessor's deal. I think it is a horrible deal, a disgusting deal that I would have never made. It is an embarrassment to the United States of America ... I have had it."
Trump to Turnbull: You're my 'most unpleasant call'
Trump said he had been speaking by phone that day to different world leaders.
He told Turnbull, "Look, I spoke to [Vladimir] Putin, [Angela] Merkel, [Shinzo] Abe of Japan, to France today, and this was my most unpleasant call, because I will be honest with you."
"Putin was a pleasant call," Trump said of the Russian president. "This is ridiculous."
Trump claims refugees detained by Australia are 'bad'
"Does anybody know who these people are? Who are they? Where do they come from? Are they going to become the Boston bomber in five years? Or two years? Who are these people?" Trump asked Turnbull.
"I hate taking these people," Trump later said. "I guarantee you, they are bad. That is why they are in prison right now."
"It's not because they're bad people," Turnbull retorted.
Trump demanded, "Can Australia give me a guarantee that if we have any problems — you know, that is what they said about the Boston bombers. They said they were wonderful young men."
"They were Russians," Turnbull said. "They were not from any of these countries."
"They were from wherever they were," Trump said.
The Boston Marathon bombers, brothers Tamerlan and Dzhokhar Tsarnaev, were born in Kyrgyzstan and raised in Chechnya, a Russian territory.
Turnball responded Friday morning to the release of the transcript, saying, "It's always better when these conversations remain confidential -- but I haven't got any further comments to make on it. As I said, it was a courteous, frank conversation."
Trump calls New Hampshire a 'drug-infested den'
Discussing how to combat drug crime with Pena Nieto, Trump said he won New Hampshire because the state "is a drug-infested den."
His comments drew ire from New Hampshire's Sen. Jean Shaheen and Gov. Chris Sununu.
The state is dealing with a drug epidemic. According to the Centers for Disease Control and Prevention, New Hampshire was second in the nation for drug overdose deaths per capita in 2015.
Trump told Pena Nieto that Mexico is dealing with "some pretty tough hombres in Mexico that you may need help with, and we are willing to help you with that, big league."
ABC News' Karen Travers contributed to this report.