The comment was quickly decried by Republican and Democratic lawmakers in the Granite State, including the state's Republican governor who endorsed Trump during the 2016 campaign.
During the call, according to the Post, Trump lashed out at Peña Nieto for the quantity of illegal drugs that come into the United States from Mexico.
"We have a massive drug problem where kids are becoming addicted to drugs because the drugs are being sold for less money than candy," Trump said.
He later bragged that he won the Granite State because of the opioid epidemic.
"I won New Hampshire because New Hampshire is a drug-infested den," he said.
Asked by CNN to comment on the transcript, Michael Anton, a spokesman for the National Security Council, said only that he "can't confirm or deny the authenticity of allegedly leaked classified documents."
Richard Baum, Acting Director of National Drug Control Policy, offered a slight defense of Trump by telling CNN that the opioid "epidemic has hit New Hampshire harder than many other states and the President saw this on the campaign trail when he met parents and visited communities devastated by opioid addiction."
Trump did, in fact, win the Republican primary in New Hampshire, more than doubling the vote total received by his nearest competitor, Ohio Gov. John Kasich. Trump, however, narrowly lost the state to Democrat Hillary Clinton in the general election.
Trump seized on the opioid epidemic while campaigning in New Hampshire throughout 2015 and 2016, promising the people of the state that he would boost local clinics, help those who are already hooked on opioids and stop the flow of drugs coming into the state.
The issue was so critical to Trump that he headlined an event in New Hampshire focused strictly on opioids days before the 2016 election.
"I just want to let the people of New Hampshire know that I'm with you 1,000%, you really taught me a lot," he said before promising to help people who "are so seriously addicted."
Republican New Hampshire Gov. Chris Sununu flatly said Trump's statement was "wrong" in a statement on Thursday.
"It's disappointing his mischaracterization of this epidemic ignores the great things this state has to offer," he said. "We are already seeing positive signs of our efforts as overdoses and deaths are declining in key parts of the state. In spite of this crisis, New Hampshire remains the best place to live, work and raise a family."
New Hampshire's two Democratic senators also blasted the comments.
Sen. Jeanne Shaheen tweeted that Trump needed to apologize to the state of New Hampshire and "then should follow through on his promise to Granite Staters to help end this crisis."
"It's absolutely unacceptable for the President to be talking about NH in this way -- a gross misrepresentation of NH & the epidemic," she wrote.
Sen. Maggie Hassan called Trump's comments "disgusting."
"As he knows, NH and states across America have a substance misuse crisis," Hassan wrote. "Instead of insulting people in the throes of addiction, [Trump] needs to work across party lines to actually stem the tide of this crisis."
And the Democratic National Committee said the comments prove that Trump "looks at the opioid epidemic as a political advantage, rather than a national crisis that demands the attention and care of our President."
The most emotional reactions came from drug treatment advocates who had dealt with addiction themselves.
Erin Canterbury, a New Hampshire Democrat who had voted for then-candidate Trump in 2016, said she was irate when she heard that Trump called New Hampshire "a drug-infested den."
"I am pretty ticked off," said Canterbury, who chose Trump after hearing him talk about his own family's history with addiction and promise to address opioid treatment issues after he won the White House. "We are drug den, really?"
The 39-year-old mother of two -- almost seven years sober after getting addicted to prescription painkillers -- said her support for Trump was already "starting to dwindle," but this latest news pushed her over the edge.
Canterbury said she now regrets her vote for Trump and likely won't vote for him in 2020.
"Mr. President, we are not a drug den, we are a state ... in a very serious health crisis, and for him to call us that is ridiculous," she said. "It's a slap in the face."
New Hampshire is one of the states most directly impacted by the opioid crisis. According to the NH Drug Monitoring Initiative, drug overdose deaths have climbed in the state since 2012 and it expected to again hit an all-time high once data from 2016 is tabulated.
A national study from the Centers for Disease Control and Prevention found that 25% of all drug overdose deaths were related to heroin in 2015. That number was just 6% in 1999.
In response to the epidemic, Trump created a White House panel tasked with looking into how the federal government should respond. The panel, which is being led by New Jersey Gov. Chris Christie, released its interim report earlier this week and suggested that Trump declare a state of emergency to combat opioids.
"Our citizens are dying. We must act boldly to stop it," read its report. "The first and most urgent recommendation of this Commission is direct and completely within your control. Declare a national emergency."
The report added: "America is enduring a death toll equal to September 11th every three weeks," noting the fact that 142 Americans die from drug overdoses every day.
Trump has made similar comments in the past about how inexpensive drugs can be.
"We're becoming a drug-infested nation," Trump said in February. "Drugs are becoming cheaper than candy bars."