"We have to be the radical left alternative. In some of the agreements we have had with the Social Democrats and the Green Party we have compromised too much. It is important that we stand up for our values," said Alexander Lowejko, chairperson of the Left Party district in Jönköping county to the newspaper.
Almost three quarters of the districts that the newspaper spoke to argued that the party should continue on its own, with many disputing Lars Ohly's position that the party has benefited by being part of the Red-Green coalition.
Several districts are critical of the party leadership and Carin Högstedt in Kronoberg county called for Ohly to go.
"We carry on in the same vein - it isn't working. We need a new leadership that is not connected to a defence of communism," she said to DN.
Other districts meanwhile expressed support for the cooperation with other parties, and others criticised the decision to pull out of talks regarding Swedish forces in Afghanistan on Monday.
"You win nothing by dropping out. I am in favour of cooperation. We are a small party and can't achieve much on our own," said Maria Malama-Fregidou, chairperson of the Left Party in Uppsala.
Lars Ohly has meanwhile given some indication that he is considering his position at the head of a party that has been in electoral decline since its record 12 percent showing in 1998 under former leader Gurdrun Schyman.
"It is a challenging task and it takes a lot of time and energy," Ohly told the Expressen daily on Monday, declining to confirm whether he would continue in the post beyond the next party congress, scheduled for 2012.