"Now he invited me for lunch. He sends me a message saying, 'Come and I invite you for lunch in New York,'" Fox said Friday on CNN's "New Day." "I will come if at first you apologize to Mexico, to Mexicans, to Mexican people. And number 2, you apologize to U.S. workers, because you're not telling them the truth."
"Sounds like you don't want to have lunch with Donald Trump," CNN's Chris Cuomo followed up.
"Well, I can have it in San Cristobal at my place," Fox replied.
Fox, who is known for his passionate responses to Trump, also criticized the real estate mogul for assuming that terrorism was behind the EgyptAir Flight 804 crash, even though authorities are still investigating the cause of the crash.
"The guy that has a very short short fuse is him. Just look at his reaction yesterday about this horrible plane crash or bomb or whatever it was," Fox said.
Trump tweeted early in the day Thursday that the disaster "Looks like yet another terrorist attack" before asking, "When will we get tough, smart and vigilant? Great hate and sickness!" a statement that Fox suggested was not presidential.
Trump's tweet came before Egyptian officials had publicly raised the possibility of a terror attack.
"First message should be of solidarity, of compassion to the people, the families of the people that was in that plane. That's where you start always," Fox added. "You don't go to war with everybody. You don't go and hate everybody. You don't see everyone as an enemy."
Fox has been a frequent critic of Trump's plan to build a wall between the United States and Mexico -- and to make the Mexican government pay for it.
He opened his interview on "New Day" reinforcing his disapproval of Trump's plan.
"Thank you for the invitation. I'm not paying for that wall," Fox said.