President Trump on Monday said the U.S. may need to pay upfront for his promised border wall because Mexico is "reluctant" to foot the bill for the billion-dollar barrier.

"One way or the other, Mexico is going to pay for the wall. It may be through reimbursement, but one way or the other Mexico will pay," Trump told reporters at a joint press conference with Finnish President Sauli Niinisto.

"We need the wall, it's imperative," he continued. "We may fund it through the United States, but ultimately Mexico will pay for the wall."

Moments earlier, the president stood by his previous threat to shut down the federal government unless Congress provides funding for the Southern border wall when lawmakers return from recess next month and turn their attention to spending legislation. A House-passed bill containing $1.6 billion in border security funding has already drawn criticism from key GOP senators who oppose the president's request.

Despite being a central pillar of his presidency, Trump has repeated refused to articulate how his administration plans to get America's Southern neighbor to cover the cost of a wall along the U.S.-Mexico border.

Trump said Monday that his administration already faces an uphill battle in trying renegotiate the North American Free Trade Agreement with Mexico, admitting that the U.S. will "probably have to at least start the termination process" before a fair deal can be brokered.

"We will either terminate or renegotiate it," he said, before turning to his Finnish counterpart to add that his country "would never have signed NAFTA" even though Finland is not located in North America.

The president's comments come hours after the Mexican government issued a statement repudiating Trump's claim that it will pay for his border wall.

"As the Mexican government has always stated, our country will not pay, under any circumstances, for a wall or physical barrier built on U.S. territory along the Mexican border," read a statement Monday from Mexico's Ministry of Foreign Affairs.

In a jab at Trump's frequent use of Twitter to conduct diplomatic matters, Mexican officials also said they "will not negotiate NAFTA nor any other aspect of the bilateral relationship, through social media or any news platform."