Sources within the four party centre-right coalition, known as the Alliance, had told Swedish Television on Thursday that it was willing to change how committee chairs are chosen.
Right now, committee chairs and co-chairs are dealt among parties on the left and right. The Alliance, however, suggested divvying them up proportionately.
That would mean the Sweden Democrats, currently polling at 20 percent, would likely head up several committees. Today, no Sweden Democrat sits on a leadership position in the Riksdag despite being the third largest party.
Once news of the proposal broke, though, parties on the left critized the move as a legitimization of the Sweden Democrats, which have remained politically isolated in the Riksdag because of their anti-immigration stance and roots in the white power movement.
Liberal Party leader Jan Björklund was the first to break away from the proposal. Followed by Center Party leader Annie Lööf, meaning it is only supported by the Moderates and Christian Democrats within the Alliance.