Friday's secret vote in the Senate on a constitutional amendment that would allow President Horacio Cartes to run for re-election sparked riots.
The protestors 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.
The proposal must also be approved by Paraguay's chamber of deputies, where 44 of the 80 members belong to the president's Colorado Party.
The measure would apply to future presidents and Cartes, a soft-drink and tobacco mogul who was elected in 2013.
Opponents of the move included Senate President Roberto Acevedo of the opposition Authentic Radical Liberal Party. "They were attacked", Interior Minister Tadeo Rojas said, blaming rioters for attacking the building and the police.
Confrontations over the weekend escalated with protesters storming the building and setting fire to furniture and paper.
The officials said- protesters were stealing things and causing damage to the offices of those who backed the bill.
President Cartes called for calm and a rejection of violence in a statement released on Twitter.
The damage to Paraguay's Congress building was substantial and the fire was reported to have raged for nearly two hours before it was finally extinguished.
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Protesters chant slogans against presidential re-elections outside the congress building, in Asuncion, Paraguay, Friday, March 31, 2017.
Since 1992 Paraguay has banned re-election in an attempt to avoid a return to dictatorships such as that of Stroessner.
Felicita de Quintana, the mother of Rodrigo Quintana, 25, who was shot dead on the eve during a protest against the approval of a constitutional amendment for presidential reelection, mourns during his funeral in Asuncion.
"A coup has been carried out", said Senator Desiree Masi from the opposition Progressive Democratic Party.
The demonstrators claimed the vote undermines the country's democratic institutions, denouncing it as "illegal".
Lugo was removed from power by the Senate in 2012 in the wake of a land dispute scandal.
But after the rioting, the president of the lower house, Hugo Velazquez, announced the vote was postponed, saying he was shocked by the violence.
Many Paraguayans are in favour of re-election eventually being passed via a gradual, deliberative constitutional reform.
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