On Monday, the Union asked Vilnius authorities to allow the rally on March 11. Julius Panka, the Union's chairman, said 5,000 people would take part in the march.
Vilnius Municipality says a decision will be made no earlier than Friday.
The Lithuanian National Youth Union had wanted to hold the march on Gedimino Avenue but Vilnius authorities refused to grant permission and suggested holding it on Upės Street a bit further from central Vilnius, since other events are planned on Gedimino Avenue.
The march organized by the Lithuanian Nationalist Youth Union is held every year and has attracted considerable controversy. Marchers chanted anti-semitic slogans on one occasion, while "Lithuania for Lithuanians" is heard every year.
