The recount of all the votes for county administrative boards and advance ballots for municipalities could be completed at around the same time.
As a result the Election Authority may then hold off on reviewing the advance ballots for the Riksdag.
"We shall have to see if we do that or if we wait until it is finally completed," said Vivan Nilsson at the authority to news agency TT.
If counting of the advance ballots is delayed, the publication of the final results from the election wouldn't take place until Thursday, a day later than normal.
Part of the uncertainty lies in the fact that election officials don't know exactly how many advance Riksdag ballots have been cast, but there were around 100,000 in the last election in 2006.
Currently, the Alliance coalition needs 7,100 more votes to attain an overall majority of votes cast. If the centre-right would receive, say, 60,000 of around 100,000 outstanding uncounted ballots, then they would have an overall majority in the number of votes.
However, it is not yet clear what this would mean in terms of the distribution of seats in parliament.
In order for Alliance to gain the three seats that they lack for a full majority, it would require the Social Democrats to lose seats in Dalarna, Värmland and Göteborg, according to Svante Linusson, a mathematics professor.
"It is within a hair's breadth," said Linusson to the Aftonbladet daily.
The newspaper details the scenarios required for the Alliance to claim a total of 175 seats required for an absolute majority (preliminary results give them 172 seats).
First, the Liberal Party (Folkpartiet) performs strongly or the Social Democrats poorly in Gothenburg and Värmland - with seven extra percent for the Liberals perhaps sufficient.
Furthermore the Left Party has to claim a seat from the Social Democrats in Dalarna.
If these scenarios were to be fulfilled then the Alliance could claim the 175 total required, the newspaper explained.
There is a possibility that the Alliance parties make up the 7,108 votes required to claim a majority of the votes, yet remain deprived of a majority of the seats in parliament - a unique occurrence under the Swedish electoral system.
According to Olle Folke, a researcher at Colombia University, the Alliance may need even fewer votes to achieve an overall majority of parliamentary seats.
"If the Alliance has optimal luck then 1,000 votes is all that is needed to give them a majority of the seats," Folke told Sveriges Radio's Ekot news programme on Tuesday.
Of the 349 seats in Sweden's Riksdag 310 are so-called permanent constituency seats with distribution based upon the number of persons entitled to vote in the various constituencies, and allocated according to the parties' share of the popular vote in the given constituency.
Furthermore there are 39 so-called adjustment seats which are distributed on the basis of the overall election results.