Mexican president Enrique Pena Nieto says Mexico will not pay for a United States border wall.
Building a 3200km wall along the Mexican border was one of Mr Trump's key proposals during his presidential election campaign.
Mr Trump said construction would start within months and Mexico would pay back to the United States "100 percent" of the costs.
Mr Pena Nieto condemned Mr Trump's order.
"Far from uniting us, it divides us," he said. "Mexico does not believe in walls."
He said Mexico would not contribute any money.
"I've said time and again; Mexico won't pay for any wall."
He said his government would do everything possible to protect the rights of migrants in the United States.
Mr Pena Nieto is under growing pressure to cancel a scheduled meeting with Mr Trump in Washington next week.
White House press secretary Sean Spicer said earlier the wall would "stem the flow of drugs, crime, illegal immigration into the United States" and Mexico would pay for it "one way or another".
Trump: Not all illegal immigrants should fear deportation
Mr Trump said illegal immigrants brought to the United States as children should not worry about deportation.
He told ABC News he had a big heart and would take care of everybody.
He said great people already in the US who had a good job should be less worried.
He said his administration would release a policy on the matter in the next four weeks.
- BBC / Reuters