Kristersson was to meet the  Parliament Speaker,  Andreas Norlen, on  Sunday morning (Swedish time).

On Friday, the Moderate party leader urged his centre-right coalition allies to help end Sweden's political gridlock by joining him in a minority government ahead of the deadline.

Writing in a Facebook post, Kristersson said he had given the other three members of the Alliance a few days to consider whether they "can and want to" join the Moderates in a government that stands for the coalition's common political agenda.

The Nordic region's largest economy produced an inconclusive election result last month, with a surge by the nationalist Sweden Democrats depriving the two traditional blocs of a majority.

Kristersson's appeal to his traditional centre-right partners follows his failure to secure the support of the Social Democrats, the biggest party in parliament. Their leader, outgoing Prime Minister Stefan Lofven, lost a confidence vote in the wake of the September 9 election and was then unable to form a new government, prompting the parliamentary speaker to hand over the mandate to Kristersson.

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After a week of talks, Kristersson has now mapped out two possible options: A full, four-member Alliance Cabinet, or an Alliance Cabinet without the Centre Party and the Liberals, which strongly oppose the idea of having to rely on the nationalist Sweden Democrats for survival.

Whatever the constellation of Alliance parties in a potential coalition, the government would "act just as a full-size Alliance government would have done", Kristersson said. He also emphasised the fact that neither the Sweden Democrats nor the Left Party would be given influence over policy.

Kristersson has until Tuesday to tell Parliament Speaker Andreas Norlen that he's in a position to be Sweden's next prime minister.

He appeared to face an uphill struggle on Friday, with Sweden Democrats leader Jimmie Akesson telling Swedish media his party would not lend its support to Kristersson unless it gets something in return.

Sweden operates under a system known as "negative parliamentarism", whereby a minority government can be in power as long as a majority of lawmakers don't vote against it.

Parties have a maximum of four attempts to form a government or face a new election within three months. The new government will need to present a 2019 budget to parliament within three weeks of assuming office, or November 15 at the latest.

Bloomberg