On 16 November 1989, Parada and 24 other DNI members visited the Central American University shortly after a massacre committed by the army killed eight people, including six Jesuits, which he condemned.

On four occasions, Parada defended El Salvador against international arbitration cases, specifically on legal matters related to the energy industry, of hundreds of millions of dollars each.

[7] According to an opinion poll published by Marketing y Tendencias on 1 September 2017, around 2 percent of ARENA members stated that Parada should be the party's presidential candidate.

[11] On 2 October 2017, Parada stated he would no longer seek ARENA's presidential nomination, arguing that the party's candidate selection process would make his campaign impossible.

His candidacy was proposed by the Sumar por El Salvador civil movement, and Celia Medrano [es], an activist and human rights lawyer, was his running mate.

[19] Parada has criticized the Armed Forces of El Salvador's (FAES) conduct during the Salvadoran Civil War, stating that it went against the law, and condemned the 1989 Jesuit murders.

We are pro-life, but there are situations where there are medical emergencies and personal decisions that the State should not penalize a woman for" ("Yo creo que el aborto es una decisión muy personal de una mujer, somos próvida pero tampoco en todas las situaciones, se van a dar emergencias que requieran tomar decisiones médicas y decisiones personales, que el Estado no debe penalizar").