"This government has run its course", Kristersson told a party rally, referring to Lofven's minority cabinet. This after an election campaign in which the Sweden Democrats were routinely branded as "racist" and "neo-Nazi" by their opponents-and by the worldwide press.
The Sweden Democrats (SD) are expected to achieve 19.2% of the vote.
The preliminary results suggest the Sweden Democrats have fallen short of expectation and that voters have not been as receptive to their anti-immigration rhetoric as it may have seemed.
Like its far-right counterparts across Europe, the Sweden Democrats party has taken pains to move into the mainstream and, to a certain extent, tone down its rhetoric in order to appeal to a broader swath of the electorate. He said his party had "won" the elections because of its gain in seats.
But he would need to overcome decades of acrimony between the two blocs and get support from parties on the centre-right, something they have ruled out.
Around 7.5 million Swedes were eligible to cast a ballot in the vote, with final results expected to be announced before midnight (22:00 GMT).
Party leader Jimmie Akesson has said there is no place for racism in the party, which in the build up to the elections called the arrival of nearly 400,000 asylum seekers into Sweden since 2012 a threat to national culture and a strain on Sweden's welfare system.
Sweden's general election on Sunday was not the colossal victory for Sweden Democrats, a political party with neo-Nazi origins, that many had feared. For me, when he is saying that immigrants are not welcome to Sweden ... he is trying to spread hate between the people. Meanwhile, next-door in Finland, the populist True Finns party was included in the center-right government in 2016.
The Sweden Democrats, a party founded by white supremacists, rose to 17.8 per cent from 12.9 per cent in the last election four years ago, in effect securing the balance of power.
Similarly, the party's proposal to only take in asylum-seekers from Nordic nations is a de facto ban on refugees that goes against Sweden's history as one of the world's most humanitarian nations.
"The alliance will not govern or discuss how to form a government with the Sweden Democrats", Kristersson said.
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.
Mattias, a Stockholm resident at an election night party in the city, said he was "extremely concerned" about the far right's steady climb since it entered parliament in 2006 with 5.7 percent. However, Lofven has said they will "organise themselves".
At the same time, the Sweden Democrats party still prides itself on its consistently hard-line position on immigration-and it proved that it could very ably inject its ideas into the political mainstream. SD has gained momentum as other established parties adopted their proposals and rhetoric.
Responding to the call, Mr Lofven said he would continue to "calmly work" in his role over the next two weeks (when parliament opens), but acknowledged the election "should be the funeral for bloc politics".
That message has resonated with a growing number of people in recent years, as concerns rose over high-profile incidents of gang violence, an influx of refugees and regional economic inequality.
In an interview with AFP during the campaign, Akesson stressed he would "lay down his terms" after the election, citing immigration policy, crime-fighting and health care as priorities. Instead, it told a more subtle but increasingly familiar tale now seen across a variety of European parliamentary systems and perhaps further afield, too - that of increasing political fragmentation and the slow decline of dominant political parties.