The governing body said it had been served a writ "despite the Scottish FA's offer to honour Craig's contract in full".
Levein, 48, a former international who became manager in December 2009, departed with Scotland bottom of their 2014 World Cup qualifying group.
Scotland had collected two points from four matches after opening draws with Serbia and Macedonia before defeats in Wales and Belgium.
"The Scottish FA has since received notification that Craig has chosen to resign, thereby foregoing the offer made to honour his contract in full," the SFA said in a statement on their website.
"In the notification received, failure to make a proposal in lieu of compensation has been cited. It is the view of the Scottish FA that no such offer is required given Craig's decision to resign, especially since an offer of mediation was rejected by his legal representatives.