Trump tweeted Sunday morning: "With Mexico being one of the highest crime Nations in the world, we must have THE WALL. Mexico will pay for it through reimbursement/other."
In response, the country's foreign ministry released a statement saying Mexico would not pay for a wall or other physical barrier at the border "under any circumstances."
"This determination is not part of a Mexican negotiating strategy, but a principle of national sovereignty and dignity," the statement said.
One of Trump's principle campaign promises was to build a wall at the southern border and have Mexico pay for it. Since taking office, Trump has called for Congress to allocate money for the wall instead and have Mexico pay the US back. Mexican leaders have publicly rejected any avenue to pay for the wall.
Earlier this month, Trump threatened a government shutdown should Congress not allocate money to build the wall that Mexico has refused to fund. The deadline for passing a spending bill to keep the government open is at the end of next month.
The Mexican foreign ministry's statement also addressed Trump's comment regarding crime in Mexico. The ministry said the crime is a "shared problem" for both countries and is caused in part by US demand for Mexican narcotics.
"Only on the basis of the principles of shared responsibility, teamwork and mutual trust can we overcome this challenge," the statement said.
The ministry also reacted to a different Trump tweet Sunday morning about the North American Free Trade Agreement.
"We are in the NAFTA (worst trade deal ever made) renegotiation process with Mexico & Canada. Both being very difficult, may have to terminate?" Trump tweeted.
Mexico said its position at the negotiating table was "serious and constructive" and sought a winning result for Mexico, the US and Canada.
"Mexico will not negotiate NAFTA nor any other aspect of the bilateral relationship through social media or the media," the ministry added.
Mexico offered any help that may be needed to deal with the aftermath of Hurricane Harvey as well.