Nationals backbencher Andrew Broad has openly accused Prime Minister Malcolm Turnbull of a failure of leadership, in another sign of growing tensions inside the federal Coalition.

Mr Broad's attack on the Prime Minister over his handling of same-sex marriage comes as Nationals MPs agitate for a commission of inquiry into the banking sector, a move that would risk destabilising the Turnbull government, which continues to resist the move.

"I think, in my view, there's been a complete lack of leadership," Mr Broad told ABC radio after the Senate emphatically rejected a series of conservative amendments to the same-sex marriage legislation on Tuesday night.

"I had a private conversation with the Prime Minister where I said, 'Have you sat down and got Trevor Evans, Warren Entsch, Dean Smith – people on the "yes" [side] – and put them in the room with Eric Abetz, Andrew Hastie and people on the "no" side? And come up with a piece of legislation that is Coalition legislation?'" he said.