Those behind the party, called Sortu, insist it rejects armed group Eta's violence and hence merits legal status and the right to field candidates in May election.
However, Spain's attorney general said it was merely a repackaged version of Batasuna, a party banned in 2003 on grounds it was part of Eta.
It is up to a special section of the Supreme Court to decide on the new party's legal status.
Protesters began marching peacefully and largely in silence through city streets in the port of Bilbao under banners reading, "Toward peace, legalisation".
"Hope has begun to enter into Basque society and we want it to be for good this time," said separatist leader Kontxita Beitia at the end of the rally.
The attorney general's office said it would file its request that the court ban Sortu by March 11. It is likely that the court will not have enough time to arrive at a ruling before May 22, the election date, which will rule them out from running in the Basque regional polls.
Should Sortu be allowed to run it would give separatist politicians access to local and regional government posts and financial benefits that come with them.
Interior Minister Alfredo Perez Rubalcaba on Friday said that the government was prepared to take steps to stop Batasuna candidates from joining other Basque parties should the court ban Sortu.
The new party's unveiling on February 7 was the culmination of intense internal debates within Eta-linked pro-independence groups which concluded that bombs and bullets were no longer an effective way to seek a Basque state independent of Spain and France.