Mexico's negotiating position will continue to be "serious and constructive" and the country's negotiators will not hash out differences "via social media or the press", the foreign ministry's statement said.
Even as he pressed for congressional approval of funding for the wall on the Mexican border, he promised that USA taxpayers' costs would be refunded.
As the first step to deliver on one of his most divisive campaign pledges, Trump signed a directive to begin the construction of the wall less than a week after taking office.
"We are in the NAFTA (worst trade deal ever made) renegotiation process with Mexico & Canada".
The president's tweet comes ahead of another round of trade negotiations with Mexico and Canada starting September 1 in Mexico City. Trump tweeted Sunday morning.
This would require additional Homeland Security personnel along the border, and tougher security measures in the face of violent crime syndicates infiltrating the US.
"The government of Mexico takes this opportunity to express its full solidarity with the people and government of the United States for the damages caused by Hurricane Harvey in Texas". Ignoring Trump's threats, Gutierrez said in a statement that "As we have done in the past, Mexico stands with Texas in this hard moment".
Republicans firmly control the House of Representatives, but have only a narrow majority in the Senate, where at least eight Democratic votes will be needed to pass a spending bill.
While it won't be providing funding for Trump's desired wall, America's southern neighbor did say it would offer whatever assistance it can as Texas and other states deal with Tropical Storm Harvey. "Why wouldn't they be", President Trump said.
"But he's not saying that Mexico is going to pay for it now", one reporter said.
"As we work with the Mexicans in other policies and trade policies and such, we'll determine ways for us to make that right", he said.
At his Phoenix rally, he threatened to prompt a government shutdown unless Congress agreed to fund the wall.