Civic rights groups Freedom Under Law and the Helen Suzman Foundation are arguing that their application to have President Jacob Zuma suspend NPA boss Shaun Abrahams is a matter of urgency.
Advocate David Unterhalter, who has been representing the organisations, has argued that Zuma should suspend Abrahams immediately, pending an inquiry into his fitness to hold office.
Abrahams made the announcement that Finance Minister Pravin Gordhan will be charged with fraud and then later withdrew those charges last month.
The deadline for them to respond is Monday 28 November.
EWN's Gia Nicolaides says Unterhalter believes the integrity of the NPA is at stake if Zuma does not act fast.
He believes the NPA's reputation has been damaged and that this is the time to take action in order to regain some integrity.— Gia Nicolaides, EWN reporter
He says the matter cannot wait... Zuma could sit on the matter for months.— Gia Nicolaides, EWN reporter
The judges have questioned the need to rush the matter along, considering Zuma has already put steps into place.
They will announce their decision on the urgency of the application after 16h00 today.
#Abrahams Court afjourns. judges will make decision by 16:15. GN— EWN Reporter (@ewnreporter) November 24, 2016
Take a listen to the EWN update: