The prime minister's comments come as pressure mounts on Finance Minister Katy Gallagher, who has denied she misled parliament in 2021 about being aware of the allegations before they were made public.
Ms Higgins says she was raped by fellow Liberal staffer Bruce Lehrmann in Parliament House in 2019, a claim Mr Lehrmann has always denied.
Mr Lehrmann's trial was aborted over juror misconduct and prosecutors did not seek a retrial, citing concern for Ms Higgins' mental health.
Responding to claims she knew about the incident for weeks and planned to use the information for political gain, Senator Gallagher has said she did not seek to weaponise the allegations.
Questions over her conduct were raised after leaked text messages between Ms Higgins and her partner David Sharaz emerged last week, suggesting the pair strategised with the then-opposition senator about how to break the story.
Mr Albanese said his minister had been transparent and the suggestion Senator Gallagher misled parliament was "absurd".
"It's a bizarre conspiracy theory that suggests that Labor is somehow at the centre of all of this," he told ABC Radio on Tuesday.
Mr Albanese said the two staffers' former boss, Liberal senator Linda Reynolds, had confirmed Senator Gallagher told her she was aware "in broad terms" about the allegations before they were publicly aired.
"So this has been known by Senator Reynolds since that time since 2021, and now, in 2023, somehow this is this concocted issue by what is a desperate Liberal opposition," he said.
As parliament resumes on Tuesday, coalition senators are set to use Question Time to target Senator Gallagher over her knowledge of the allegations.
Opposition Senate leader Simon Birmingham said because Labor previously chose to ask hundreds of questions about the Higgins matter, questions being asked now about who knew what were warranted.
"The claims that there was no knowledge of any information were made to the senate ... it's only appropriate that that should be cleared up and addressed in the senate by (Senator Gallagher)," he told Sky News.
Asked about claims made by Fiona Brown, the former chief of staff for Senator Reynolds, that ex-prime minister Scott Morrison misled parliament over his knowledge of the case, Senator Birmingham said Mr Morrison's ministerial career was over.
Senator Birmingham added it would have been far preferable for police to be involved in the case at the earliest possible stage and for legal proceedings to have been allowed to run their course.
The ACT is holding an inquiry into the investigation and prosecution.
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