Cabinet Minister Christopher Pyne has acknowledged the simmering tensions between Prime Minister Malcolm Turnbull and his predecessor Tony Abbott, admitting that the two still disagreed about "who the prime minister should be".

Mr Pyne and fellow Liberal frontbencher Josh Frydenberg had on Friday sought to play down the rivalry that had descended into open warfare in Parliament on Thursday over a supposed deal on gun imports, when the Defence Industry Minister made the admission.

Of the spat between Mr Turnbull and Mr Abbott, Mr Pyne said: "They are very old friends. Of course they have a difference of opinion about who the prime minister should be. That's been played out in public, we know that, and Malcolm Turnbull is the prime minister."

In a separate interview, Mr Frydenberg labelled the skirmish a "great big distraction" and a "beltway" issue that was of little interest to voters outside the Canberra politics bubble.