Maduro made his remarks on Friday, also calling Duque a satellite ally of the United States.
"I do not engage in assaults on other people, I protect democracy, freedom and [I do] what all the states, protecting democracy, should do — condemn the abuses of dictatorship," Duque said on Friday, as quoted by the Tiempo newspaper.
The Colombian Foreign Ministry, in its turn, responded to Maduro's remarks about Duque by calling on the Venezuelan government to respect the Colombian president.
"The Foreign Ministry considers these statements as the assault on the dignity of the Colombian president, representing the Colombian people who elected him," the ministry said in a statement on Friday.
The relations between Colombia and Venezuela have been strained. They escalated further after the assassination attempt on Maduro, in which the president was unharmed and seven Venezuelan soldiers sustained injuries, in August.
Caracas accused Bogota, particularly Colombian ex-president Juan Manuel Santos, of having a role in the attack. Moreover, Venezuela said it would put blame on Colombia for any future attack on its territory. The Colombian Foreign Ministry denied any involvement of Bogota in the assassination attempt on Maduro.