Paraguayan President Horacio Cartes has said he will no longer seek re-election next year, after his bid to change the constitution triggered deadly riots.

Cartes said in a statement on Monday that he will "in no event" try to run in the April 2018 vote, seeking to end a political crisis unleashed by his push to remain in power another five years.

Presidential re-election has been taboo in the South American country since the 35-year dictatorship of General Alfredo Stroessner ended in 1989.

After senators passed an amendment last month to change that, opposition activists stormed Congress, ransacking politicians' offices and setting them on fire.

Police shot dead one opposition activist in a raid during the riots. Hundreds of people were injured and more than 200 arrested.

That triggered calls for crisis talks, backed by Pope Francis. But they fell apart when the main opposition, the Liberal Party, boycotted them.

OPINION: Why was Paraguay's Congress burning?

Cartes said he hoped his "gesture of renunciation" would "deepen the dialogue aimed at strengthening this republic's institutions," the AFP news agency reported.

But the opposition said the conservative president's Red Party had not gone far enough.

"The only way to believe the president's statements is if the ruling party shelves its attempt to amend the constitution," said the speaker of Congress, Liberal Party politician Roberto Acevedo.

But Red Party spokeswoman Lilian Samaniego said party leaders had decided against withdrawing the amendment.

Cartes' attempt to change the constitution had the backing of his leftist rival Fernando Lugo, who was president from 2008 to 2012 and also wants to run again.

But the Liberal Party bitterly opposes changing the 1992 constitution's limit of a single five-year term.

Cartes' change of heart came as international pressure mounted against his re-election bid.

One of US President Donald Trump's top envoys for Latin America, Francisco Palmieri, the assistant secretary of state for Western hemisphere affairs, is going to Paraguay for talks on Tuesday.

And Luis Almagro, the secretary-general of the Organization of American States, is expected on Thursday.