He served as Secretary General (Chief of Staff) of the Presidency during the government of Rómulo Betancourt. After that, he was part of the National Congress. During Rafael Caldera's Presidential administration, Velásquez served as Minister of Communications from 1969 until 1971. From 1984 to 1987 he was President of the Comisión para la Reforma del Estado (COPRE), the Commission on the Reform of the State. Between 1989 and 1993, he chaired the "Comisión Presidencial para Asuntos Fronterizos con Colombia", Presidential Commission for border issues with Colombia (COPAF). At the time of his death, he was a board member of the New York-based Human Rights Foundation.