Authorities said 30 people, including some opposition leaders, were injured in unrest in the capital after senators approved the bill in a secretive vote.
Opposition leaders denounced the vote Friday as a "parliamentary coup," saying it could clear the way for a return to dictatorship in the landlocked South American nation of 6.8 million people.
Furious protesters broke into the Congress late Friday, ransacking lawmakers' offices and starting fires after senators approved a proposal to allow the president to run for re-election.
The measure requires approval in the lower house, the Chamber of Deputies, which delayed a vote originally set for today.
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The interior ministry said in a statement that "the authorities are investigating the circumstances of the death, which is presumed to have occurred at the hands of a member of the National Police."
Police raided the party offices after activists took refuge there during a night of riots, Alegre said.
The injured included three lawmakers, according to firefighters and an opposition senator. Police said 211 people were arrested, some of them minors.
To chants of "Dictatorship never again!" hundreds of protesters clashed with riot police, who used mounted units and water cannon to disperse them.
Calm was restored around 0400 GMT Saturday. Large numbers of police remained on alert.
Cartes's allies in the upper house of the legislature passed the bill on Friday, sidestepping resistance from opponents.
Opposition senator Luis Wagner said those injured included Senate speaker Roberto Acevedo, lawmaker Edgar Ortiz, who was hit in the mouth by a rubber bullet fired by police, and Liberal leader Alegre, who lost to Cartes in the 2013 presidential elections.
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