The four companies which are affected are Avia Express, Avitrans Nordic, Golden Air and Svenska Direktflyg and the strike is set to continue until June 9th if the parties are unable to reach agreement.
The Swedish Airline Pilots Association (Svensk Pilotförening - SPF) rejected the mediators' offer on Friday and a final attempt to resolve the conflict failed on Sunday.
"SPF demands for an agreement which meets the basic security needs of Swedish pilots has not been met by the mediator's offer," said association chairperson Gunnar Mandahl in a SPF statement on Sunday evening.
"It's too late to stop the strike now. There are such complex and difficult issues to consider so an agreement will be made by tomorrow at the earliest," Mandahl said.
It is not yet clear how many flights that are affected and if an agreement is not reached then the strike action will be extended to all of the association's 2,000 members on Wednesday, affecting foreign and charter travel.
"It will affect SAS, Norwegian and charter travel with Fritidsresor and Apollo from 5am to 1pm on Wednesday," Mandahl told The Local on Monday.
Airports across Sweden are currently effected by the strike.
"All our airports are affected to some degree, with the biggest impact felt in Bromma and Ronneby, which have the greatest number of departures," said Anders Broad Sell, spokesman for Swedavia which owns and operates 14 of the country's major airports.
"Furthermore all the minor airports are affected, for example those owned by local municipalities," he said.
At the heart of the conflict is the vexing question of the airlines' right to hire temporary agency workers. Employers have called for changes in existing collective agreements, with some negative impact for existing employees, the union said.
"The offer cuts pilot pay by 15-20 percent and at the same time increases working hours from 40 to 47.5 hours a week," SPF wrote in its statement.
Avia Express has sacked all of its 80 pilots from July 17th and would like to hire external pilots.