NT Coroner Elisabeth Armitage has been investigating Mr Walker's death since September 2022, and was set to resume on Monday October 23.
Mr Rolfe shot the 19-year-old three times while on duty in the remote community of Yuendumu but was acquitted of murder in a five-week trial last year.
Mr Rolfe's lawyer, Luke Officer, filed a submission two weeks out from the resumption of the inquest asking the coroner to consider recusing herself from the inquest on the grounds of apprehended bias.
The North Australian Aboriginal Justice Agency, Mr Walker's family, Northern Territory Police and the Yuendumu Parumpurru Committee all urged the coroner not to step aside.
In a statement, the court said the coroner did not have time to sift through the hundreds of pages of submissions in time for Monday's sitting.
"Coroner Armitage will need to take time to carefully consider the matters raised in the many submissions received before ruling on the application, in circumstances where she has other court obligations this week," the statement said.
"The further delay to these proceedings is extremely regrettable but necessary to address the application made."
Next week's sitting has been vacated and no alternative date has been set.
In its submission, NT Police said Rolfe's application was a delaying tactic to avoid giving evidence at the inquest on Monday.
Mr Rolfe argued the coroner colluded with police to have him sacked earlier in the year to provide "justice" for Mr Walker's family.
In a reply filed late on Tuesday evening, Mr Rolfe's lawyer defended the application.
"The description of a serious submission as a forensic tactic is unjustified," Mr Officer said.
The court and Ms Armitage visited the remote community of Yuendumu and met with Mr Walker's family and community members last year.
Mr Rolfe's lawyers said the coroner could have "distanced herself" from the grieving families, particularly from conversations about punishing Mr Rolfe for killing Mr Walker.
"Discussions had taken place during the proceedings about the need for payback and that there would be no healing until the blood of Mr Rolfe had been split," Mr Officer said.
Mr Officer said the way the coroner and counsel assisting engaged with the community was unnecessary.
"There is a marked distinction between the conduct of a culturally appropriate inquest and the Coroner's engagement," he said.
The inquest into the Warlpiri man's death has been repeatedly disrupted by legal stoushes about whether Mr Rolfe and another officer have the legal right to refuse to provide evidence to the coroner.
Mr Rolfe previously refused to answer controversial questions on the grounds they may expose him to disciplinary action, while he was still in the force.
Judge Armitage ruled that witnesses could not decline to answer questions, and appeals by Mr Rolfe in the NT Supreme Court and the Court of Appeal were unsuccessful.
The rulings meant the coroner could now be able to compel Rolfe to answer questions about racist text messages that the inquest was told he sent.
The coroner is set to make her decision next week as to whether to excuse herself.