The party has published its application to intervene in the Scottish Government’s court battle over an independence referendum.
It wants permission to make written submissions and “short oral submissions” during the hearings scheduled for October 11 and 12.
It comes after Lord Advocate Dorothy Bain, Scotland’s top law officer, referred a prospective referendum Bill to the UK Supreme Court to determine if it is within Holyrood’s powers.
The legal arguments centre on differing interpretations of the Scotland Act 1998, which says matters relating to the Union are reserved to Westminster.
First Minister Nicola Sturgeon wants to hold a referendum in October next year, but the UK Government has refused to agree to this.
In a 15-page application to the court, lawyers Claire Mitchell QC and David Welsh argue it would be “fair, just and reasonable” to allow the SNP to intervene in the proceedings.
They said the SNP’s arguments are intended to complement, and not detract from, those of Ms Bain.
The application raises a number of issues, including the party’s past manifesto commitments and election victories.
It argues the right to self-determination is one that is “fundamental and inalienable”, and says the SNP’s position is the Scottish Parliament “does have the legislative competence to legislate for a referendum on Scottish independence”.
The application echoes arguments put forward by Ms Bain that a referendum on independence would be to ascertain the views of the Scottish people and would not automatically implement the result.
“The applicant regards it of fundamental importance to these proceedings that it be recognised that the holding of a referendum, such as that which is being proposed, does not of itself implement the result or the outcome of that referendum,” it says.
"The referendum indicates the view of the demos on the question posed to it.
"That there will be subsequent secondary discussions between the UK and Scottish governments in the event that the Scottish people indicate their support for Scottish independence does not change that.
"Those discussions are separate from the referendum and do not inform its purpose.”
The application says the “referendum itself is not an act of secession; it is not a unilateral declaration of independence”.
It adds: “Put short, the holding of a consultative referendum does not result in a reduction in the scope of the powers of the UK Parliament and nor does it, of itself, have any effect on the Union.
"Legislation to enable such a referendum does not, therefore, in the respectful submission of the applicant, relate to the reservation of the Union nor to the Parliament of the United Kingdom.”
SNP business convener Kirsten Oswald said: “The SNP’s application is now with the Supreme Court.
"It is intended to support and complement the arguments for the Bill being within the Scottish Parliament’s competence that are set out in the Lord Advocate’s written case.
“The SNP’s application focuses on the inalienable right of all nations to self-determination, which is enshrined in the United Nations charter and argues that the Scotland Act should be interpreted in a way that upholds rather than denies that right.
“The Bill raises a fundamental issue of democracy – in line with the principle of self-determination, Scotland’s future must be decided by those who live here, not dictated by Westminster politicians.
“It is now for the Supreme Court to determine whether our application to intervene should be granted.”