Right-wing President Horacio Cartes is seeking to reform the constitution to let him run for office again in an election in 2018 after his current term ends.
His allies in the upper house of the legislature passed the bill yesterday, sidestepping resistance from opponents who say the bill clears the way for dictatorships.
To chants of "Dictatorship never again!" hundreds of protesters clashed with riot police and broke into the congress building, battering down entrances and fences and shattering windows.
Firefighters said some 30 demonstrators and police were hurt in the disturbances.
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Opposition senator Luis Wagner said those injured included senior opposition politicians such as Senate speaker Roberto Acevedo.
Acevedo has challenged the bill in the Supreme Court, arguing it is unconstitutional.
The measure was scheduled to be considered Saturday in the lower house Chamber of Deputies, where the president has a majority.
But after the rioting Chamber president Hugo Velazquez announced that the vote was postponed, and said he was shocked by the violence.
Paraguay is still recovering from the 35 year-long dictatorship of general Alfredo Stroessner (1954-1989).
Since 1992 the country has banned re-election in an attempt to avoid a return to dictatorship.
By removing the ban, the reform will also allow left-wing former president Fernando Lugo to run again for office. He held power from 2008 to 2012.