The chief prosecutor, Eva Finné has given investigators the task of questioning Assange who is suspected of one case of molestation.
"I don't know when this will happen," Finné told news agency TT.
The first allegation against 39-year-old Julian Assange, concerning the more serious charge of rape was dismissed already on Saturday. Finné has now also dismissed suspicions of molestation in this case.
Eva Finné stressed that this does not mean that she doubts the veracity of the woman's account.
"But the content of the interview does not support the contention that a crime has been committed," Finné said. The preliminary investigation in this case has thus been closed.
Molestation is an offence which would normally incur a fine but a prison term up to a year is the maximum permitted penalty. The law describes the offence as "anyone who physically or by other reckless means molests another".
Claes Borgström, the lawyer representing the two women involved, has criticised the prosecutor's decision to close the other investigation and plans to ask for the decision to be examined tomorrow.
"That which at one time was classified as rape is according to the prosecutor not even a matter of sexual molestation and according to my understanding it is patently clear that there is a reasonable suspicion of that," said Claes Borgström.
Borgström also thinks that the prosecutor should have interviewed the plaintiff before making her decision. He is also unhappy that the alleged offence has been classified as molestation and not sexual molestation.
Borgström said that he planned to appeal the decision.
According to Borgström both of the women involved in the allegations met Julian Assange in connection with his lecture tour of Sweden. They are both aged 25-35-years-old and the women have said that Assange was sober when he molested them.
Leif Silbersky, one of Sweden most high-profile defence lawyers, was on Monday employed to defend Assange.
Silbersky has argued that the case has taken on unreasonable proportions and places the blame with the duty prosecutor, Maria Häljebo Kjellstrand, who issued a warrant for Assange's arrest after the women approached the police with their allegations on August 13th.
"This is a scandal, he has been stigmatised across the world as a rapist and it comes down to a crime punishable with a fine when a competent prosecutor considers the case," Silbersky told news agency TT.