The President of Paraguay, Horacio Cartes, says he will no longer seek re-election after his bid to change the constitution triggered rioting.
He said he had been inspired by Pope Francis's call for peace and dialogue.
Demonstrators set fire to the Congress building last month in protest at a secret Senate vote to allow second terms.
Paraguay suffered under decades of dictatorship until 1989 and many oppose presidential re-election.
Senators say they will continue to campaign for a vote in the lower house.
They argue that Paraguay is the only country in Latin America that does not allow second terms and it needs to modernise its constitution.
During the riots, police shot dead a demonstrator which triggered calls for crisis talks backed by Pope Francis.
They fell apart when the main opposition, the Liberal Party, boycotted them.
The conservative president had the backing of his leftist rival Fernando Lugo, who was president from 2008 to 2012 and also wants to run again.