President Nicolás Maduro of Venezuela has warned that he would respond to any U.S. military action with an “armed fight” and claimed that Secretary of State Marco Rubio was trying to draw President Trump into a war in the Caribbean that would mar his reputation.

“Mr. President, Donald Trump,” the Venezuelan leader said on Monday, “watch out, because Mr. Rubio wants to stain your hands with blood.”

The statements, made from Caracas during Mr. Maduro’s first news conference in over a year, come amid rising tensions between Venezuela and the United States. In late August, the United States began moving warships and troops into the Caribbean, near Venezuelan waters — which the Trump administration has said was to combat drug trafficking.

But the size of the military buildup has led to speculation over whether the real goal is to oust Mr. Maduro, through military action or other pressure.

Mr. Rubio said recently that “for the first time in the modern era,” the U.S. government was “truly on the offense” against organized cartels sending drugs to the United States. He and other officials in the Trump administration have called Mr. Maduro an illegitimate leader and his government a “narco-terror cartel.”

Jimmy Story, a former U.S. ambassador to Venezuela during Mr. Trump’s first term, said in an interview that using so much military might to take out drug trafficking boats was a bit like “using a blowtorch to cook an egg.”