Mexico has threatened to sever diplomatic ties with Venezuela as relations between the two worsen.
Mexico says Mr Chavez's comments strike at the dignity of its people
The Mexican government says President Hugo Chavez must apologise for describing his Mexican counterpart as a puppy dog for US imperialism.
But, on his weekly TV and radio show this Sunday, Mr Chavez warned President Vicente Fox "not to mess with him".
The row began last week, after Mexico supported a failed US bid to relaunch regional free trade talks at a summit.
During his Sunday programme, the Venezuelan president again condemned Mr Fox for allegedly violating protocol in trying to press for an agreement on the Free Trade Area of the Americas (FTAA) when it was not on the Summit of the Americas' agenda.
He also accused the Mexican leader of disrespecting him.
The Mexican government said that Mr Chavez's comments "strike at the dignity of the Mexican people" and demanded a formal apology from Venezuela.
On Wednesday, Mr Chavez said that Mr Fox had, as he put it, been left bleeding from the Summit of the Americas earlier in November.
At the meeting, the US and Mexico were unable to win backing for a resumption of talks on the FTAA.
They faced opposition from five of the 34 countries attending, among them Venezuela and the host, Argentina.
The other 29 nations - including Mexico - said they wanted to resume talks on the free trade agreement in 2006.
Speaking before an audience of supporters and businessmen in the Venezuelan capital, Caracas, Mr Chavez said: "How sad that the president of a people like the Mexicans lets himself become the puppy dog of the empire."
The Mexican government immediately called in the Venezuelan Ambassador, Vladimir Villegas, for a meeting to explain Mr Chavez's comments.
The foreign ministers from the two countries discussed the dispute on Friday, but later Mexico said more work needed to be done to resolve the row.