The ANC has described Jacob Zuma as a "law-abiding citizen who has consistently respected the courts", calling on the public to be patient and allow the court to deal with the former president's corruption matter.
On Tuesday, the KwaZulu-Natal High Court in Pietermaritzburg issued a warrant of arrest after Zuma failed to appear for the sitting of his fraud and corruption case.
His legal team told the court he was too ill to appear.
Judge Dhaya Pillay questioned the strength of the proof presented to the court by Zuma's lawyers.
Pillay said it appeared the dates on the document had been altered.
She said Dan Mantsha, acting for Zuma, could not clarify certain questions that she had.
"The date is altered to be January 6, but there is no initialing of that date. It is not clear that ZK Motene, who signed this document, is indeed a registered medical practitioner. Mr Mantsha assumes it is his medical practice number. That is guess work."
Mantsha questioned why the judge would not accept the medical certificate.
"Why would the court doubt a medical certificate from the military hospital? [That] is disappointing. I will have to talk to the doctors with Zuma if he is in a condition to listen to this, then we will engage. I will get advice from his medical team."
Mantsha said his client was being victimised and persecuted.
While Pillay has issued a warrant, it won't be executed before Zuma's next court appearance on May 6, 2020.
Zuma will have to tell the court why he did not appear on Tuesday.
Criminal law expert James Grant says if Zuma fails to appear at the next court appearance, the warrant will be triggered, forcing law enforcement to arrest him.
On Wednesday morning, the ANC released a statement saying it had "noted developments around court proceedings" regarding Zuma.
It said it respected the court's decision, without explicitly saying the judge issued a stayed warrant of arrest.
"Former President Jacob Zuma is a law-abiding citizen who has consistently respected the courts and submitted himself to judicial processes regardless of his stature. He has always co-operated with law-enforcement agencies whenever asked to do so," ANC spokesperson Pule Mabe said in a statement.
Mabe concluded the statement by appealing to members of the public "to exercise patience and allow Former President Jacob Zuma and the courts to deal with the matter when it resumes again on the 6th of May 2020".
The statement did not make any reference to Zuma's condition or his whereabouts.
Meanwhile, the Presidency has declined to comment on the matter.