Left leader Jonas Sjöstedt said he would speak to Ulf Kristersson and Ebba Busch Thor of the conservative Moderate and Christian Democrat parties to appeal for support in such a situation, but ruled out turning to the far-right Sweden Democrats.
The Left Party would need seven additional votes from MPs to trigger a no confidence vote.
“No, I am not planning (to speak to the Sweden Democrats), but Ulf Kristersson and Ebba Busch Thor would both be asked,” he said in an interview with Sveriges Radio.
A months-long parliamentary deadlock over the new government was ended on Friday when Stefan Löfven was voted back in as prime minister after the Social Democrats and Greens reached an agreement with the Centre and Liberal parties, who will allow the two former parties to govern in exchange for slightly more right-wing economic policies.
The Left Party allowed Löfven to be voted in after being given reassurance that they will not wholly lose their political influence on issues not covered by the four-party deal.
If Left, theoretically, brought down the government with the help of the Moderates, the leader of the Moderate party Ulf Kristersson would be the next prime ministerial candidate in line.
That would likely require the Centre and Liberal parties to return to the hitherto conventional alliance with the two other right-of-centre parties in the conservative Alliance bloc.
“One thing I trust completely is that the Social Democrats want to govern. And they are not going to make proposals that will prevent them from governing,” Sjöstedt said.
“It is clear that we have many thoughts about how to prevent inequality increasing in Sweden, and that includes the fact that we have, this week, spoken intensively with unions and tenants’ associations, and forged plans on how we can use the tools at our disposal to influence the path taken in parliament,” he said.