UPDATE 2-Swedish Left Party reject housing compromise, PM Lofven set for no-confidence vote

(Adds Left Party response)

STOCKHOLM, June 20 (Reuters) - Sweden's Prime Minister Stefan Lofven on Sunday appeared to have failed to stave off a no-confidence vote on Monday he is likely to lose after the Left Party dismissed his compromise for a new system of setting apartment rents.

Lofven earlier on Sunday offered a compromise that would mean counterparts in the housing market would work to reach an agreement for a new rent-setting model for new production, which has been the norm in Sweden.

"We are giving the counterparts an opportunity to find a solution. We now expect that other political parties are prepared to be responsible and not plunge Sweden into a political crisis," Prime Minister Stefan Lofven told a news conference.

However, the proposal was quickly dismissed by the Left Party.

"One of the counterparts is negotiating with a gun held against its temple," Left Party Leader Nooshi Dadgostar told Swedish Radio. "We are heading towards a no-confidence vote. I find it concerning that they are so determined to raise people's rents."

Sweden has a rigid system using collective bargaining for setting rents. Centre-right parties have long tried to loosen the rules and let the market decide rental prices for newly-built apartments, which would affect roughly 1% of Sweden's apartments.

Earlier this week the opposition Sweden Democrats called a vote of no confidence scheduled for Monday, which Lofven looked set to lose after the Left Party withdrew its support for the government over a proposal to ease rent controls on newly built apartments. (Reporting by Johan Ahlander and Anna Ringstrom; Editing by Emelia Sithole-Matarise and Louise Heavens)