JOHANNESBURG (REUTERS) - South Africa's Constitutional Court on Thursday rejected Olympian Oscar Pisitorius' right to appeal against his conviction for the murder of girlfriend Reeva Steenkamp.

The Supreme Court of Appeal upgraded the 29-year-old's conviction to murder in December after the state prosecutors appealed the athlete's prior conviction of culpable homicide in the Pretoria High Court.

South African authorities had challenged Pistorius' appeal on the grounds that the Supreme Court of Appeal had correctly found Pistorius guilty.

The athlete, nicknamed "Blade Runner" because of the prosthetic legs he uses to race, had filed papers to appeal against his conviction at the Constitutional Court, the country's highest court, on Jan 11.

"We can confirm that Oscar Pistorius' leave to appeal has been denied," National Prosecuting Authority spokesman Luvuyo Mfaku told Reuters.

Anneliese Burgess, the Pistorius' family spokeswoman, said she had just heard the news and would issue a statement after consulting with the family.

Tania Koehn, the lawyer for the Steenkamp family, told local TV news channel eNCA that they felt that: "The law must take its course."

"They don't want to comment any further," she added.

Pistorius shot and killed Steenkamp on Valentine's Day in 2013, and has spent the last few months under house arrest at his uncle's home in Pretoria while awaiting his appeal.

Pistorius now faces a possible minimum 15-year jail sentence for the murder of his girlfriend.

It is likely that a date for Pistorius' sentencing could be set on April 18, when he was due to appear in court to give an update on his appeal at the constitutional court.