In the leaders' telling, though, the calls never happened -- and the White House has belatedly agreed.
It was an unusual pattern of pushback against the President of the United States, a frequent and expansive telephoner who sometimes hands out his personal cell number to the people he meets. And it raised questions about which presidential assertions can be believed and which cannot.
On Wednesday, the White House responded to questions about the calls with the same answer: the conversations actually took place in person.
"I wouldn't say it was a lie. That's a pretty bold accusation," press secretary Sarah Huckabee Sanders told reporters at the White House. "The conversations took place, they just simply didn't take place over a phone call."
Her answer came after both the Mexican government and the Boy Scouts contradicted Trump's claims that he took calls from their leaders.
On Monday, Trump heralded a call from Mexico's president about a decrease in border crossings.
"Even the President of Mexico called me," Trump asserted in the Oval Office on Monday after swearing in his new chief of staff. "Their southern border, they said very few people are coming because they know they're not going to get to our border, which is the ultimate compliment."
In Mexico, however, officials recalled a different version of events.
"President Enrique Peña Nieto has not been in recent communication via telephone with President Donald Trump," read a statement from the Mexican President's office.
The two leaders did meet in person on the sidelines of last month's G20 meetings in Hamburg, Germany, and did discuss migration, Peña Nieto's office said.
Sanders said it was that meeting that Trump was referring to when the President mentioned a phone call.
"He was referencing a conversation they had at the G20 summit, where they specifically talked about the issues that he referenced," Sanders explained on Wednesday.
The Mexican presidential authorities also said Peña Nieto offered Trump a different set of figures than the ones he claimed: a 31% decrease in repatriations of Mexican citizens from the United States over the past six months and a 47% decrease in migration from central America into Mexico.
Boy Scouts take issue
It wasn't the only disputed phone call of the week. The Boy Scouts of America, which has already apologized for Trump's politically-tinged speech at its annual Jamboree, said none of their leaders phoned the President afterward to praise his appearance -- counter to Trump's own version of events.
"I got a call from the head of the Boy Scouts saying it was the greatest speech that was ever made to them, and they were very thankful," the President told The Wall Street Journal last week, according to a transcript obtained by Politico
An official with the Scouts said on Wednesday they were not aware of any phone calls between the group's leadership and the President.
And they said their statement last week apologizing for the political tone of Trump's remarks still stood.
"The Chief Scout Executive's message to the Scouting community speaks for itself," the organization said in a statement.
Michael Surbaugh, the Chief Scout Executive of the Boy Scouts, wrote last week that he "regrets that politics were inserted into the Scouting program" after Trump used his address to the gathering to go after his 2016 opponent, Hillary Clinton, and accuse the media of bias.
Sanders again said the discussion happened in person. She did not specify who Trump spoke with.
"Multiple members of the Boy Scouts leadership following his speech there that day congratulated him, praised him and offered quite powerful compliments following his speech," Sanders said Wednesday.