Cabinet minister Christopher Pyne has hit out at his "cowardly" colleagues privately briefing the media urging former Speaker Bronwyn Bishop to retire and cautioned against a ludicrous "Salem witch trial" of MPs over entitlements as further questions about the use of taxpayer-funded expenses swirl.

Mr Pyne's cabinet colleague Eric Abetz says Labor frontbencher Tony Burke, who led the opposition's successful pursuit of Mrs Bishop over her lavish use of travel perks, should be considering his own position over his use of entitlements.

Mr Burke has repaid several travel entitlements he incorrectly claimed and says early on in his career he misunderstood the rules.