The leader of Sweden’s third largest party -- the centre-right Moderates -- was formally asked to try and form a new government on Monday by the speaker of parliament.
That new government will likely include the far-right anti-immigrant Sweden Democrats either as a formal coalition partner or providing support to the government in a so-called "confidence and supply" agreement.
In Sweden's 11 September election, the country's right-wing parties secured 176 seats in the Riksdag; while left-wing parties combined only got 173 seats in a closely-fought election.
Now, the speaker of parliament has charged Moderates leader Ulf Kristersson to try and form a coalition government, without setting a deadline to do it.
“My message to the speaker has been that everything is going well," Kristersson told reporters after meeting with the speaker of parliament. “I want to form a government that unites, not divides.”
The leader of the Sweden Democrats, Jimmie Åkesson, also met the speaker and said afterwards that "it would suit Sweden to have a majority government. That is my take.”
The question is now what coalition can reach a majority. One of the centre-right parties has said it does not want to be in a coalition with the right-wing Sweden Democrats, a party founded in the 1980s by far-right extremists that now is the country’s second-largest in parliament.
Different centre-right combinations are possible but it seems clear that the Sweden Democrats will have significant leverage in any centre-right government.
With climate change denial and a strong anti-migrant stance, it could push to override the policies of the outgoing centre-left government, say experts.
"(Even) if they are a parliamentary backing outside of the government, that it will still give them quite a substantial veto power over policies that are pursued by the government," said Göran von Sydow, Director of the Swedish Institute for European Policy Studies (SIEPS).
Von Sydow believes the Sweden Democrats will also attempt to influence policies at the EU level.
"They are a Eurosceptic party, which means that they are reluctant that any other issues become part of the European decision-making when they are deemed to be better dealt [with] at the national level," he said.
"But, also in the big issues, we are facing - such as climate, and the environment - they are perhaps less ambitious. They have been less outspoken when it comes to issues of rule of law, and they are very sceptical about giving more room to social policy and those kinds of issues at the European level."
The Sweden Democrats have tried to move toward the mainstream in recent years, standing this year on a platform of cracking down on crime and strictly limiting immigration.
Sweden has seen an increase in gang violence in recent years, and this year so far there have been 273 shootings, 47 of them fatal, according to police statistics. The shootings also wounded 74 people, including innocent bystanders.
Last week, Sweden’s Social Democratic Prime Minister Magdalena Andersson acknowledged losing the election. She will continue in a caretaking capacity until a new government is formed.