STOCKHOLM — Two questions dominate Swedish politics after elections this month yielded a stalemate: Who will violate a campaign pledge? And will it result, for the first time, in a government that has support from a nationalist party with neo-Nazi roots?

Just one seat separates the governing coalition of the left from the center-right coalition that is the main opposition — but each fell far short of a majority. Both blocs have sworn not to make a deal with the Sweden Democrats, the right-wing, anti-immigration party that now controls enough seats to play kingmaker.

“The bourgeois and left-wing blocs are playing a game of chicken right now,” said Lars Tragardh, a history professor at Ersta Skondal Bracke University College.

Prime Minister Stefan Lofven hopes to form a new government by luring smaller parties away from the center-right alliance, but they say they are still committed to their coalition. The two blocs could form a “grand coalition,” but so far, they are not talking. The center-right group has demanded that Mr. Lofven resign, but he has not budged.