Sweden's general election on 13 September saw the far-right Sweden Democrats suffer their first loss of voter support since first entering parliament 16 years ago. The party slipped from being the country's second biggest party to its third. The centre-left Social Democrats appear poised for a return to power, although it could take months for their leader, Magdalena Andersson, to form a coalition. Strong results for the left and green parties gave her left bloc a wafer-thin, three-seat majority. This was reported by Qazaqyia.kz citing The Guardian.

The result comes alongside the situation in Germany. A week earlier, in the German state of Saxony-Anhalt, the far-right Alternative for Germany (AfD), officially classed as "extremist", stood on the brink of power for the first time since the Nazi era. In Sweden, a party with neo-Nazi roots has been pulling the government's strings for the last four years. The general election was set to show whether the far right would be formally brought into government, or whether enough Swedes would opt for a gear change, having seen the Sweden Democrats' hardline (some would say poisonous) agenda in action.

Votes were still being counted on Wednesday but it was immediately clear that the far-right Sweden Democrats had suffered a setback; their first loss of support among voters since it entered parliament for the first time 16 years ago. The party slipped from being the country's second biggest party to its third.

The centre-left Social Democrats appear poised for a return to power, although it could take months for their leader, Magdalena Andersson, to form a coalition. Strong results for the left and green parties gave her left bloc a wafer-thin, three-seat majority.

Is the far right's regression, however modest, a turning point? Have Swedes reached the limits of a taboo-busting experiment with populist, nationalist rightwing prescriptions? And is there a message for mainstream leaders across Europe, many of whom seem fatalistic about a continental far-right surge? France goes to the polls in April while governments in Italy, Spain and Poland all face their electorates later next year.

The Dutch political scientist Cas Mudde says elections in one country are a poor guide to what will happen in another. Specific local factors in Sweden, including a scandal, may have dented the far right's support. For Mudde, the scale of the AfD's win in Saxony-Anhalt, however, was "a black day for Europe" – and with far-right ideas gaining ground across the continent, he warned mainstream politicians that "today's key fight is for democracy, rather than for party or power".

This is where Sweden offers a cautionary tale. Its political establishment had "fully normalised" the far-right party, Mudde said. "Its nativism is now shared by all the major parties, albeit in lighter form, from the Moderates on the right to the Social Democrats on the left."

But the decline in the far right's support, for now, he thinks, "at the very least creates space for mainstream parties to focus on issues other than immigration".

Ann-Cathrine Jungar, a professor of political science at Södertörn University in Stockholm, is very sure that the Sweden Democrats are not on the way out. Electoral rankings go up and down, she said, and the party's influence will endure. More important now is how the mainstream parties respond.

"We focus a lot on the extreme and radical right parties, but the key to their influence is what the other parties do. Why have Sweden's mainstream parties adopted the far right's policies? The Social Democrats have co-opted their ideas, even though they are counter to the country's needs. In Sweden, we need competent, talented people who want to come and live here, we need labour for health and social care. Yet nationalism seems to be the prevailing ideology now."

In a widely read Guardian essay headlined How Sweden lost its soul – and stopped being Sweden, published before the vote, Martin Gelin documented his country's transformation after 2022. Rightwing parties that year signed a Faustian pact with the Sweden Democrats, buying its support for a minority rightwing government. The deal? The far right was given a direct hand in shaping policy. "A new Sweden has emerged, cruel and cold for migrants", wrote Gelin, with xenophobic and ethno-nationalist ideas "now comfortably embedded in the political mainstream".

Most shockingly, Andersson's Social Democrats, modelling themselves on their hardline Danish counterparts, had bought into the far right's framings on crime and immigration.

Will Sweden's Social Democrats now learn from their worst performance in more than 100 years, and embrace an agenda that does not involve deporting toddlers to Iran, people with dementia to the UK, or locking up 14-year-olds?

Jungar is sceptical. "When it comes to linking crime and immigration, this is the new normal," she said. "The Social Democrats will not pursue policies that are more liberal."

Yet the political centre in Sweden could articulate a clear alternative to the far right, Mudde says. The Left and the Greens did significantly better among young voters in this week's election. "This reflects a development we see across Europe, namely that young people prefer outspokenly leftwing parties over centre-left parties."

Ulrich Siegmund (centre), head of the AfD state parliamentary group in Saxony-Anhalt, celebrates his party's election win with parliamentary leaders Alice Weidel (left) and Tino Chrupalla (right).