Australian Federal Police Commissioner Reece Kershaw on Tuesday revealed the force's ACT policing arm was moving closer to completing its investigation.
"I have been informed by the ACT chief police officer that a brief of evidence is likely to be provided to the director of ACT public prosecutions in the coming weeks," he told Senate estimates.
Mr Kershaw took aim at critics of the police response to the March 2019 incident, saying suggestions the AFP had taken a backward step risked dissuading victims from coming forward.
"It would be a travesty if that was to occur," he said.
Department of Prime Minister and Cabinet secretary Phil Gaetjens, tasked with investigating who in Scott Morrison's office knew about the allegation and when, faced questions in a separate hearing.
Mr Gaetjens paused his inquiry after speaking with Mr Kershaw about the potential for overlap with police work.
The top public servant has now resumed his probe and expects to complete his work within weeks.
"I'll finish as soon as possible," Mr Gaetjens told parliament.
Labor is concerned about a cover-up after Mr Gaetjens said it would be up to the prime minister whether the report would be made public.
He is yet to interview Ms Higgins but says he plans to after she asked to be involved.
The powerful bureaucrat refused to reveal how many people he spoke to during the investigation or if staff in the prime minister's office were receiving legal representation.
Government Senate leader Simon Birmingham said Ms Higgins deserved for the process to run its course.
"Brittany Higgins deserves to have a thorough process completed, one that is of integrity," he said.
Senator Wong questioned whether Senator Birmingham had no shame over inquiries being dragged out and questions not being answered at the estimates hearing.
Mr Kershaw said ACT Policing had told him there was no problem with a crossover between the two investigations.
"Mr Gaetjens did make the right call in suspending his inquiry but I did want to make sure there was no problematic intersection with the criminal investigation," he said.
In response to a question on notice from Labor senator Kristina Keneally, the AFP also revealed Peter Dutton's office was told in October 2019 about the incident.
The AFP confirmed direct contact with Mr Dutton was not made until February 11 this year, backing up the senior cabinet minister's account.