The decision by the Chamber of Deputies, where President Horacio Cartes has a majority, went towards a key condition set by the opposition before talks could begin Wednesday involving parties and the church.
The violence broke out last Friday after senators approved a bill that would allow Cartes to run again for office in 2018 when his current term ends.
After rioters stormed Congress, police hunted down protesters. One 25-year-old activist was apparently shot by police as they searched the offices of the opposition Liberal Party.
After firing his interior minister and police chief over the death, Cartes on Monday reached out to the opposition, proposing negotiations to calm tensions.
Pope Francis on Sunday lent his support to the talks and the Catholic Church has made available one of its buildings close to the presidency for the meeting.
Liberal Party leader Efrain Alegre -- a probable presidential candidate in 2018 -- said the talks could only go ahead if the bill were withdrawn.
Continuing public anger at the amendment push resulted in some 10,000 people protesting late Monday in front of Congress. Other protests took place in the capital.
The specter of a long run of dictatorships throughout most of the 20th century hangs over the tiny South American country, population nearly seven million.
For some, the moves to change the constitution revived memories of authoritarian power grabs.
The 1992 constitution underpinning Paraguay's young democracy fixes a one-term limit on presidents.
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