"The conditions do not exist that allow us to cooperate with the Finns led by Halla-aho," Sipila said on Twitter, referring to Jussi Halla-aho, who was named the party's new leader on Saturday.
Though the governing coalition, in power since May 2015, has not formally collapsed it appeared likely to splinter. The conservatives and centrists could now enter into talks with possible new partners.
Participating in the three-party coalition has come at a heavy price for the Finns party.
Its support has more than halved from 17.7 percent in the May 2015 general election to 8.4 percent in a February poll by Taloustutkimus.
A member of the European Parliament, Halla-aho has said he would push the two other coalition parties to toughen their immigration policies.
He wants to steer his party further to the right, which could mean pulling out of the coalition government the Finns joined in 2015.
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