The DA has applied for leave to appeal a judgment dismissing its attempt to have President Jacob Zuma's appointment of Menzi Simelane as National Director of Public Prosecutions set aside.

MP James Selfe said on Wednesday the party believed it had a strong legal case and that a higher court could come to a different conclusion.

"The Democratic Alliance has studied the judgment carefully and has consulted its legal team," Selfe said in a statement.

"The case concerns issues that are of such critical importance to the future of our country and to the integrity of our legal system that we believe we have a responsibility to appeal this judgment."

Earlier this month the High Court in Pretoria dismissed the DA's bid to have Zuma's decision to appoint Simelane as national prosecutions boss set aside. The party had argued Simelane was not "a fit and proper person" for the job.