During the US President's call with Australian Prime Minister Malcolm Turnbull on Saturday, Trump objected to an agreement over the US receiving refugees, sources told CNN. All this a day after a call with Mexico's President, where a transcript showed Trump complaining about Mexico's "handling" of "tough hombres."

Australia is an ally of the United States, with the two countries joining three other English-speaking countries in an intelligence sharing arrangement known as the "Five Eyes."

Refugee deal

The disagreement came as the two leaders discussed a deal, reached under the Obama administration, for the US to accept refugees from Australia who are living on islands in detention centers off the mainland due to strict government policies.

Many of them are from the seven countries affected by Trump's travel ban . Trump on Friday also suspended the entry of all refugees for 120 days, along with indefinitely suspending the entry of Syrian refugees.

Sources say Trump insisted it was a very bad deal for the US to take 2,000 refugees and that one of them was going to be the next Boston bomber.

Turnbull told Trump several times the agreement was for 1,250 refugees, not 2,000. He also said Australia was asking to submit them to the US for refugee screening, and if the refugees did not pass the US screening process, they would not come.

Trump expressed concern as to how this agreement from President Barack Obama's administration would go forward given his executive order the day before temporarily suspending the US refugee program.

Trump abruptly ended the call because he was unhappy, a source told CNN. White House press Wednesday night, Trump tweeted, "Do you believe it? The Obama administration agreed to take thousands of illegal immigrants from Australia. Why? I will study this dumb deal!"

Do you believe it? The Obama Administration agreed to take thousands of illegal immigrants from Australia. Why? I will study this dumb deal! — Donald J. Trump (@realDonaldTrump) February 2, 2017

Turnbull said the call ended "courteously" in a radio interview Thursday.

On Thursday, Trump used his remarks at the National Prayer Breakfast -- an annual tradition attended by many world and religious leaders -- to weigh in on the reports circulating on his phone calls.

"When you hear about the tough phone calls I'm having, don't worry about it. Just don't worry about it. They're tough. We have to be tough. It's time we're going to be a little tough, folks," he said. "We're taken advantage of by every nation in the world, virtually. It's not going to happen anymore. It's not going to happen anymore."

The Washington Post was the first to report on the details of the Australian call.

When asked about the tweet labeling the agreement brokered with Obama's administration a "dumb deal," Turnball said, while the deal may not have been one Trump would've done or considered a "good deal," the President and his administration have committed to honor it.

Earlier this week, Spicer said the Trump administration would honor the agreement, saying the refugees would be submitted to "extreme vetting."

Turnbull attempted to keep some semblance of diplomacy, declining to elaborate on details of the call.

"Look, I'm not going to comment on a conversation between myself and the President of the United States other than what we have said publicly, and you can surely understand the reasons for that," he said. "I'm sure you can understand that. It's better these conversations are conducted candidly, frankly, privately. If you'll see reports of them, I'm not going to add to them."

One person familiar with the circumstances on Saturday notes that President Trump's phone call with Turnbull came after a long day of conversations with other foreign leaders -- Turnbull was the fifth call after conversations with Japanese Prime Minister Abe, French President Hollande, German Chancellor Merkel, and Russian President Putin, each of which lasted close to an hour.

Trump, this source said, was feeling some fatigue after his first major bout of diplomacy. And while his earlier conversations weren't necessarily contentious, they did involve some tense moments. Merkel and Hollande pushed back on the travel ban over the phone. Merkel felt she had to explain the Geneva Convention to Trump -- a lecture a source has said Trump chafed at.

JUST WATCHED Mexico's top diplomat responds to Trump's tweet Replay More Videos ... MUST WATCH Mexico's top diplomat responds to Trump's tweet 00:45

'Tough hombres' talk with Mexican President

CNN has also learned details about the Friday phone call between Trump and Peña Nieto, who canceled an in-person visit with Trump after the US President insisted Mexico pay for a border wall between the two countries.

According to an excerpt of the transcript of the call with Peña Nieto provided to CNN, Trump said, "You have some pretty tough hombres in Mexico that you may need help with. We are willing to help with that big-league, but they have be knocked out and you have not done a good job knocking them out."

Trump made an offer to help Peña Nieto with the drug cartels.

The excerpt of the transcript obtained by CNN differs with an official internal readout of the call that wrongly suggested Trump was contemplating sending troops to the border in a hostile way.

The Associated Press report said Trump threatened to send US troops to stop criminals in Mexico unless the government did more to control them, but both the US and Mexican governments denied details from the story.

Sources described the AP's reporting as being based upon a readout -- written by aides -- not a transcript.

Spicer described the call with Peña Nieto as "productive."

A government official familiar with Trump's interactions with foreign leaders said, "(Trump's) interactions are naive in that he keeps suggesting we will have the best relationship ever with a broad departure of countries, but there is no substance to back it up. When he encounters a policy challenge, like with Turnbull, he responds with a tantrum."