Yes, if the couple both attend the interview and declare themselves in agreement to obtain a legal separation.

The couple then need to submit a written agreement regarding assets and liabilities or a court ruling regarding official settlement procedures (if there are assets in the marriage).
The couple also need to declare an agreement on the legal domicile of their child or a summons in a custody case, an agreement on child maintenance payments, or claim a child maintenance ruling in seperate proceedings, as well as an agreement regarding alimony payments/or an agreement of no alimony payments.

A permit for legal separation costs ISK 5,400.

Further information on legal separation/divorce can be found here.