Both the left-leaning bloc led by the Social Democrats and the centre-right bloc in which the Moderates is largest of four parties have said they would refuse to consider the Sweden Democrats as a coalition partner.
But while there was a sense of relief among supporters of mainstream parties about the nationalist group's more limited than expected gains, the election underscored a broader shift to the right in one of Europe's most socially progressive nations.
We asked political scientist Nicholas Aylott, an associate professor at Södertörn University, how the provisional result changes expectations. These results were predicted, as were the subsequent talks among the parties.
The election had been watched closely for signs about the extent to which a cascade of anti-immigrant fear could hit even Sweden, which has always been one of Europe's most open nations toward refugees.
"We need a cross-bloc cooperation", he told party supporters on Sunday evening.
So now the hard part: how to form a government. Far-right leaders in Austria, Italy and France hailed the Sweden Democrats' results.
Prime minister and party leader of the Social Democrat party Stefan Löfven waves at an election party in Stockholm, Sweden, on Sunday.
On the centre right, the Conservatives could potentially work with the Liberals, the Centre Party and the Christian Democrats. So far, he has been rebuffed, but depending on the final vote count, there may be some give, especially since at the local level nearly all parties have already been working together with the Sweden Democrats for some time.
The opposition Moderate party is also unable to take over because even an established alliance with the centre-right parties doesn't make up the numbers needed for a majority.
Nevertheless, their leader Jimmie Akesson told a party rally: "We will gain huge influence over what happens in Sweden during the coming weeks, months and years". "They come from a bad place, awful wars".
Before the vote, Prime Minister Stefan Lofven said: "This election is a referendum about our welfare".
"I will not exclude any alternative to the [present] government". During this election, almost all of Sweden's major political parties-including the Social Democrats and the Moderates-agreed that Sweden should massively reduce migrant arrivals until a Europewide immigration and refugee policy could be reached.
The two large parties have lost votes in a further fragmentation of the party system.
"This is where it gets very interesting".
The result is however so tight, with just some 30,000 votes separating the two blocs, that it may take until Wednesday (12 September) when the last votes cast by Swedes overseas have been counted and the result finally checked before a final result is known.
Swedes began voting this morning (Sunday 9) in an election dominated by fears over asylum and welfare, with the anti-immigration Sweden Democrats vying to become the biggest party.
But it would then be under constant threat from the Sweden Democrats, out to topple it at the first opportunity.
"That frankly, is an extremely implausible scenario - why would the left bloc consent to an Alliance government when the left bloc is actually a touch bigger than the alliance?"
The current situation makes it totally unclear who will end up as prime minister in Sweden.
In Sweden, the influx of 163,000 asylum seekers in 2015 has polarised voters, and could give the Sweden Democrats, a party with roots in the neo-Nazi fringe, a veto over which parties form the next government.
"The leader made the point that they are now a force to be reckoned with".
"But of course you have to think about the nature of political debate in Sweden, and the parameters of what can be said at any time".
Sweden's struggles have captured attention around the world, including in the United States, where President Donald Trump has at times held it up as an example of the failures that come from too much immigration.
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