Trump also took aim at the outlines of a deal to legalize the status of legions of illegal immigrants who arrived in the U.S. as children, and called on Congressional Republicans to exercise a "nuclear option" to toughen immigration. Last fall, Trump canceled the Deferred Action for Childhood Arrivals , colloquially referred to as DACA.

Via Twitter, the president ripped the U.S.'s southern neighbor for doing "very little, if nothing" to stem illegal immigration and narcotics from flowing across the border. He repeated a threat he made earlier this year, warning that successful trade pact renegotiations may hinge on Mexico making efforts to secure its side of border.

President Donald Trump on Sunday explicitly linked his proposal to build a barrier between the U.S. and Mexico to ongoing NAFTA negotiations, as he renewed a warning that the flow of illicit drugs and undocumented immigrants from the country "must stop."

In Mexico, presidential front-runner Andres Manuel Lopez Obrador launched his bid for the country's highest office by signaling that if he won the July 1 election, he would be less accommodating toward Trump than the ruling Institutional Revolutionary Party, or PRI. The party has lagged in opinion polls over its failure to contain violence and corruption.

"Mexico and its people will not be the pinata of any foreign government," Lopez Obrador said in a speech to thousands of people at a speech near the U.S.-Mexico border, where attendees reportedly jeered and swore at the mention of Trump.

With increasing regularity, the president has gotten more aggressive in his negotiating tactics. On several occasions, he's hinted at trying to force Mexico to pay for the proposed border wall, an idea that Mexican officials have emphatically rejected.

Just last week, Defense Secretary James Mattis spoke with Trump about using military funds to pay for the proposed wall, in the wake of the president signing a $1.3 trillion omnibus spending bill that fell short of fully funding the president's request for border security. The budget busting legislation alienated many conservatives, and put Trump on shaky footing with some of his most ardent supporters.

For much of 2017, the White House floated the idea of a border adjustment tax on Mexican goods, a proposal that met stiff resistance in Congress before it was ultimately killed in tax reform talks.

Meanwhile, talks to renegotiate the trade pact between the U.S., Canada and Mexico have gotten increasingly contentious. In theory, a NAFTA termination letter would start the countdown for a 6-month process to abrogate the pact. However, some think Washington could use such a move to gain leverage over Canada and Mexico.

In January, Mexico threatened to leave the negotiations altogether if Trump triggered the process to withdraw from the pact.

--Reuters and CNBC's Amanda Macias contributed to this article.