Australia Post has admitted contacting the City of Melbourne and Pauline Hanson after more than 100 One Nation-branded stubby holders were not delivered to locked-down public housing tower residents.
But the agency denies its chief executive threatened the council or contacted Senator Hanson directly about the hold-up.
Senator Hanson dispatched the 114 stubby holders in July with a note that read: "No hard feelings."
Days earlier, she labelled residents of the Melbourne towers drug addicts and alcoholics, claiming they were from war-torn countries and English was probably their second language.
Council officials overseeing the government-enforced lockdowns intercepted the parcels and decided against delivering them, concerned they could further inflame tensions.
In an email first published by the Nine newspapers, Australia Post warned the council it would notify the police unless the parcels were delivered without delay.
Australia Post claimed this did not amount to a threat and denied chief executive Christine Holgate personally intervened.
At the time, One Nation senators were considering whether to vote in parliament in favour of overturning a temporary relaxation of postal delivery rules.
"Australia Post confirms that Ms Holgate did not speak to Senator Hanson or One Nation on this matter, nor did she threaten Melbourne City Council," the agency said in a statement on Thursday.
But the agency confirmed it contacted both the City of Melbourne and Senator Hanson about the matter.
Australia Post said the agency took its obligation to deliver mail seriously.
"Upon subsequently being made aware the items did not reach their ultimate destination, we raised it with the City of Melbourne and engaged with the sender (Senator Hanson) in good faith to resolve the matter," it said.
"Commonwealth laws prohibit any conduct which interferes with the mail, and make it clear that Australia Post is obliged to complete the delivery of Australians' mail to the designated address."
Senator Hanson dismissed the controversy and used it to market more One Nation merchandise.
"Talk about a storm in a stubby cooler," she said.
But the postal union said the unusual episode raised serious questions about Senator Hanson "running dead" on allowing the doubling of delivery times during coronavirus lockdowns.
The union has previously claimed the rule relaxation could see up to one in four posties sacked.
"Deteriorating postal services have been forced through under the cover of COVID-19 and the community deserves to know why," national secretary Greg Rayner said.
"Workers and the community must be told the truth about special treatment for Senator Hanson."
Labor accused Ms Holgate of helping One Nation push "inflammatory and divisive" material onto vulnerable people.
"We need to get to the bottom of why the Australia Post CEO was working so hard to please Pauline Hanson," Labor frontbencher Andrew Giles said.