STOCKHOLM, Oct 2 - Sweden's parliament speaker on Friday asked Magdalena Andersson, the leader of the Social Democrats, to again try to form a new government, despite her saying on Monday she was unable to secure enough backing to do so.

Andersson's centre-left bloc won 176 seats to 173 for Prime Minister Ulf Kristersson's right-wing coalition in a September 13 election, but the four parties that won disagree over who should be allowed to be part of the new government.

Andersson's announcement on Monday followed the Left Party's decision over the weekend to back a Moderate Party candidate for parliament speaker, which she said had undercut her attempt to build a government.

Parliament speaker Andreas Norlen on Friday said the political and parliamentary conditions were the same now as when Andersson was first given a mandate.

"It is exactly the same election result, the same distribution of seats, and the same parties that are designating her as their leading candidate for prime minister... so it is reasonable for her to resume her exploratory talks," he said.

Andersson is due to report back to the speaker by October 12, either by replying or asking for an extension. If Andersson were to ask for an extension it is a matter of discussion how long that extension can be, Norlen said. A vote in parliament will definitely take place after her second attempt, he added.

There is little indication so far that Kristersson would face fewer obstacles to form a government, needing to win the backing of at least one centre-left party while retaining the support of the far-right Sweden Democrats.