"It is an incredibly unique and strange position to have, and it is completely unacceptable," said Sjöstedt at a press conference on Monday. "We are a condition for this government to be formed, and then to believe you can say that we will have zero influence.. we just don't accept it"
The Social Democrat party is pushing for another four years of government together with their partners the Greens. Both the Center and Liberal parties have promised to support this government in return for promises of tax cuts, tax breaks and measures to benefit business - assurances that have angered the Left Party.
Sjöstedt said that if the speaker of parliament wants a candidate for a prime minister vote this Wednesday, then it should be Moderate Party leader Ulf Kristersson instead.
That's because, as things stand, the Left Party can not vote for Löfven.
Radio Sweden spoke Daniel Bernmar, leader of the Left Party in Gothenburg, Sweden's second biggest city, to hear his thoughts on the party's position.