The Helen Suzman Foundation and Freedom Under Law want to force President Jacob Zuma to suspend NPA head Shaun Abrahams because they do not believe he has any plans to do so.
"The president must be forced to decide on the issue in a determined time," the two organisations' legal representative David Unterhalter said in the High Court in Pretoria on Thursday.
Zuma and Abrahams are opposing the groups' bid.
FUL and HSF brought the matter following a decision by Abrahams not to push forward with charges against Finance Minister Pravin Gordhan and two former SARS officials Oupa Magashule and Ivan Pillay. This was in connection with an early retirement for Pillay, which Gordhan signed off on in 2010 when he was at SARS.
Earlier this month Zuma wrote to Abrahams asking him to provide reasons why he should not be suspended.
The Presidency said Zuma gave notice of his intention to request reasons as to whether to suspend Abrahams, Director of Public Prosecutions Sibongile Mzinyathi and Acting Special Director of Public Prosecutions Dr Torie Pretorius.
Unterhalter told the court on Thursday: "He [Zuma] just says this is my process, they must reply by the 28th then I will make a decision. We are saying now is the time to act."
His clients are pushing the president to act urgently against Abrahams and the two other NPA officials, claiming their continued stay was causing irreparable harm to the institution.
"You cannot put a pilot who has shown incompetence back in the cockpit," Unterhalter said.
He said Abrahams had crashed the office of the NPA in terms of leadership. He also argued that the matter was about objective facts and not subjective discretion.
A full bench of the court is hearing the matter.
Judge President Dunstan Mlambo on Thursday raised some concerns over the urgency of the application, given that it involved events which had taken place in the past.
The matter continues.
