A judge in South Africa refused on Friday to grant prosecutors permission to appeal the six-year prison sentence she gave the double-amputee sprinter Oscar Pistorius, saying an appeal would not have a reasonable chance of success.

Mr. Pistorius, who is serving the prison sentence for the murder of his girlfriend, Reeva Steenkamp, in 2013, did not appear in court.

Last month, the judge, Thokozile Matilda Masipa of the High Court in Pretoria, gave Mr. Pistorius a six-year term, far shorter than the 15-year minimum sought by prosecutors.

She cited mitigating factors, including Mr. Pistorius’s disability, his expressions of remorse, his status as a first-time offender and the circumstances of the shooting.