Prime Minister Scott Morrison has made a defiant pitch to supporters of Pauline Hanson, telling them their legitimate frustrations can best be resolved by voting for the Coalition, while shaming One Nation for soliciting millions in donations from the US gun lobby.

Mr Morrison is facing a damaging split in the Coalition over whether to deny preferences to One Nation at the May election - a debate turbocharged on Tuesday after explosive reports that the minor party sought to weaken Australia's gun laws in exchange for cash.

News network al-Jazeera published video from a three-year undercover sting operation in which One Nation operatives James Ashby and Steve Dickson met senior representatives of the National Rifle Association under the guidance of a fake Australian gun lobbyist.

Another video shows Mr Ashby and Mr Dickson discussing how they would benefit from an influx of $20 million in cash, boasting they would "have the whole government by the balls" and declaring they wanted to be "in bed with the United States".