MEXICO CITY — Vice President Joseph R. Biden Jr. delivered a blunt message on Monday to leaders in Latin America who are contemplating opening the door to the legalization of illicit drugs: The United States will not budge in its opposition.

Mr. Biden, beginning a two-day trip to Mexico and Honduras ahead of a regional summit meeting next month, told reporters that he welcomed a debate over legalization, but then he knocked down the arguments in favor of it.

He said he sympathized with Latin American leaders who are frustrated over violence tied to the drug trade and with the consumption habits in its biggest market, the United States. But the few potential benefits from legalization, like a smaller prison population, would be offset by problems, including a costly bureaucracy to regulate the drugs and new addicts, Mr. Biden said.

“I think it warrants a discussion. It is totally legitimate,” he said. “And the reason it warrants a discussion is, on examination you realize there are more problems with legalization than with nonlegalization.”