Michael Adebolajo has lost the first stage of a bid to challenge his conviction and sentence for the murder of soldier Lee Rigby.
The Judicial Office said permission to appeal was refused by a judge, but that Adebolajo has renewed both appeals.
The Court of Appeal will now consider both applications at a hearing in London.
Adebolajo was sentenced in February to a whole-life term for the murder of Rigby, who was mowed down and hacked to death in Woolwich in May 2013.
Adebolajo's friend Michael Adebowale, 23, was jailed for a minimum term of 45 years for his role in the 25-year-old's death.