His left-wing opponents say the constitutional change would raise the risk of a return to dictatorship for a country that transitioned to democracy in 1989 after 35 years of military rule.
In a televised address, Cartes called on lawmakers and political leaders from across the political divide to join in a dialogue along with church leaders.
"I propose to open a broad debate, the only condition for which is the will to come to an agreement for a lasting democracy," he said.
A left-wing opposition activist was shot and killed by police in a raid on his party's offices after the riots erupted late Friday.
Protesters had earlier broken into the Congress in anger after senators loyal to Cartes approved the reform.
Cartes is seeking to amend the constitution to enable himself to run for office again in 2018 after his current term ends.
Removing the ban would also allow left-wing former president Fernando Lugo to run again. He held power from 2008 to 2012, when he was removed after an impeachment trial.
After the Senate sidestepped opposition resistance and approved the bill, it was due to be voted on Saturday in the Chamber of Deputies, where the president has a majority.
That vote was postponed after the violence, but was expected to go ahead on Tuesday.
Civil groups opposed to the reform called for a vigil outside Congress on Monday to protest ahead of that vote.
The leader of the main opposition Liberal Party, Efrain Alegre, said his side would only join in talks if the bill is withdrawn.
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