One Nation has asked Australia's intelligence agency ASIO and the Australian Federal Police to investigate the matter, citing concerns about foreign interference.
"Al Jazeera are a state owned propaganda arm of the Qatari government that supports Islamic extremist groups and are not a legitimate media organisation," the party said in a statement on Tuesday morning.
The footage, recorded on hidden cameras, captures Pauline Hanson's chief of staff James Ashby and the party's Queensland leader Steve Dickson during meetings with powerful gun advocates.
"We get the balance of power, very simply that means that we have the testicles of the Government in our hand at every given stage," Mr Dickson was heard saying in the meeting with the NRA.
"And guns, in the scheme of things, are still going to be the be-all and end-all."
Prior to the meeting Mr Ashby, who was banned from Parliament after an altercation with a senator last month, was recorded outlining what he hoped to achieve from the trip.
"If the NRA want to rally their supporters within Australia, that's one start," Mr Ashby said.
"Two, I'd love to get my hands on their software. And three, if they can help us with donations, super."
As part of the investigation, Rodger Muller, an Australian undercover reporter, set up a fake group called Gun Rights Australia and arranged the meetings between One Nation and the NRA.
When Mr Muller pressed the One Nation pair about their hopes to secure political donations, Mr Ashby said $10 million could deliver the minor party eight Senate seats.
"I mean, that guarantees you the balance of power, you'd have the whole government by the balls," Mr Dickson responds.
NRA's response to a massacre
It's unclear if any money was secured out of the trip and two months later, Senator Pauline Hanson backed legislation to outlaw foreign donations.
"Overseas money should not have an influence on our political scene, so I believe that foreign donations should be totally stopped," Ms Hanson said.
During the meeting, the NRA provided an insight into their approach when a mass shooting occurs.
"Say nothing," one official tells the One Nation men, before urging them to go on the "offense, offense, offense".
The official suggests smearing gun control advocates by making comments such as "how dare you stand on the graves of those children to put forward your political agenda?".
"I love that, thank you," he can be heard saying.
One Nation's statement said the party strongly supports the "rights of lawful gun ownership within Australia".
"One Nation members have always complied with the law."
The covertly recorded footage was used to make a documentary How to Sell a Massacre, which was aired internationally by Al Jazeera on Monday night and will air on the ABC in Australia on Tuesday night.