Swedish Prime Minister Stefan Lofven lost a mandatory confidence vote in parliament on Tuesday meaning he will step down.
Voters delivered a hung parliament in the September 9 general election with Lofven's centre-left bloc garnering 144 seats, one more than the centre-right opposition Alliance.
The anti-immigration Sweden Democrats, with 62 seats, sided with the Alliance to back the vote to remove Lofven, but it remains unclear whether they will back an Alliance government.
After Lofven is officially ousted, the speaker is likely to task Moderate Party leader Ulf Kristersson with forming a new government.
But in order to pass legislation through parliament, some MPs on the right wing would like the Alliance to cooperate with the Sweden Democrats, now the country's third-biggest party.
For two of the four Alliance parties - the Centre and Liberals - that option is unacceptable.
They have said they would quit the Alliance if the Moderates and Christian Democrats were to negotiate a deal - for example on immigration - with the far-right in exchange for their support.
Another alternative would be for the Alliance to reach a compromise with the Social Democrats on big political issues, such as the autumn budget.
Centre Party leader Annie Loof said Monday: "If an Alliance government is to take power in this current situation, cross-bloc support is needed... for economic policies as well as reforms."
Stefan Lofven's Social Democrats have ruled out backing an Alliance government, and Sweden Democrat leader Jimmie Akesson repeated on Tuesday his party would bring down any government that does not give it a say on immigration, healthcare, pensions and crime policy.
He said: "If Ulf Kristersson wants to be prime minister it can only happen with my help."
The speaker will have four attempts at finding a new government and if the situation remains deadlocked, Sweden will hold another election within three months.
With a new vote unlikely to change the situation much, some kind of compromise is likely to be thrashed out.
A number of party combinations have been suggested, but all would have a heavy political cost and a deal is could take weeks.
Lofven will lead a transition government until a new administration is installed.