Paraguay's main leftist opposition party boycotted talks launched by President Horacio Cartes on Wednesday aiming to settle a row over his bid for re-election which sparked deadly riots last week.
Cartes called for talks with various political leaders to calm tensions after police shot dead an opposition activist in a raid during riots that erupted after senators approved his election reform.
Several smaller opposition parties attended the talks, which are also supported by Pope Francis.
But the leader of the main opposition Liberal Party, Efrain Alegre, said he would not sit down with the government until congress drops the constitutional reform bill.
Alegre was one of dozens injured by the police's rubber bullets in the weekend unrest.
"We are not going to take part in a dialogue unless people are brought to account" for killing the activist and injuring other protesters, Alegre said.
Pro-government senators sidestepped opposition resistance to approve the reform on Friday and had planned to pass the bill to the lower house of Congress on Saturday.
But that vote was postponed due to the violence. Some of his allies in the congress have since dropped their support for the bill.
After firing his interior minister and police chief over the activist's death, Cartes on Monday reached out to the opposition, proposing negotiations to calm tensions.
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.