The protesters stormed the Congress and set fire to the building.
The authorities have arrested four police officers after a protester, Rodrigo Quintana, was killed.
Political leaders on Saturday paid their respects to the dead man.
His body was laid out at the headquarters of the opposition Liberal party in the capital, Asuncion.
They condemned the killing and called for an investigation into his death.
Around 200 protesters were detained but many have since been released.
The protesters had taken to the streets following a private meeting of 25 senators - a slight majority of the house - which approved a bill to amend the constitution.
Paraguay was controlled by military ruler General Alfredo Stroessner, who seized power in a coup, from 1954 until 1989.
The current constitution, created in 1992 after the dictatorship, limits the head of state to a single five-year term.
Protesters were angered by the bill which would have allowed President Cartes' to remove the restriction and run for re-election.
An opposition senator, Desiree Masi, called the move a coup and called on supporters to resist it.
The bill must also be approved by the other house of parliament - the chamber of deputies - where President Cartes' party holds a majority.
President Cartes' term is due to end in 2018.

The 37-year-old was detained following a joint investigation between Lancashire Police and the RSPCA.
A member of the public filmed the dog being punched at about 15:15 GMT on 10 December in Hendon Road, Nelson.
The RSPCA said the dog - an adult female Staffordshire Bull Terrier cross - has been checked over by a vet and is now in the charity's care.
RSPCA Inspector Charlotte Booker thanked people for their response to an appeal and said: "It has been absolutely huge over the last 48 hours and we are very grateful for the scale and quality of this response.
"The same name came forward various times so we were able to verify information quickly. I'd also like to thank Lancashire Police for their help in this joint operation."
Paraguay's President Horacio Cartes has sacked the interior minister and the chief of police after violent protests on Friday against a bill that would allow the president to run for a second term in office.
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A man has been arrested on suspicion of animal cruelty after a dog was attacked on a Lancashire street.