Pence made his claims in an opinion piece for the Miami Herald.
"I strongly reject repeated and false accusations by vice president Pence and other #US officials of Cuban military 'training,' 'controlling' or 'intimidating' in #Venezuela. These are gross lies, part of the vicious McCarthyist propaganda campaign launched by #US," Rodriguez wrote on Twitter on Friday.
The foreign minister added that Havana and Caracas enjoyed relations based on mutual respect and solidarity without interfering in each others' internal affairs.
Venezuela is currently embroiled in political turmoil.
In January, opposition leader Juan Guaido, backed by the United States, declared himself the interim president of Venezuela after disputing Maduro’s re-election last May. Washington immediately endorsed Guaido, called on Maduro to step down and seized billions of dollars’ worth of Venezuela’s oil assets.
Maduro has accused the United States of trying to orchestrate a coup in order to install Guaido as a puppet leader beholden to Washington. US-backed forces attempted to overthrow Maduro's predecessor Hugo Chavez in a failed coup in 2002. Russia, China, Cuba, Bolivia, Turkey and a number of other countries have voiced their support for Maduro as the only legitimate president of Venezuela.