Mr Pyne caused a stir after boasting of the supremacy of his moderate Liberal faction on the sidelines of a party meeting in Sydney last Friday.
He also suggested the legalisation of same-sex marriage could occur "sooner than everyone thinks" and revealed he had voted for Mr Turnbull at "every" leadership ballot he ran for despite being in Mr Abbott's leadership circle.
Former prime minister Tony Abbott said on Wednesday Mr Pyne's speech, which was leaked to the media, was "remarkably ill-advised and indiscreet" and could not have come at a worse time for the government.
"I can understand why some of my colleagues might be saying his position as Leader of the House is difficult to maintain but this is a matter for the prime minister," Mr Abbott said.
Mr Pyne responded on Wednesday night, saying he was sorry his remarks had caused such a distraction.
"I apologise to anyone they have offended. My remarks were ill chosen and unwise and I can see how unhelpful and damaging they have been," the South Australian MP said in a statement.
Mr Abbott has breathed new life into conservative forces, questioning the government's climate policy and commitment to economic reform and urging the party to stick to its same-sex marriage plebiscite policy.
On Thursday he will deliver a speech questioning a multi-billion-dollar submarine contract with French firm Naval Group, formerly known as DCNS, and urging a Plan B based on nuclear-powered subs.
"I think I have a role as a standard bearer for Liberal conservative values here and in the wider world," Mr Abbott told radio 2GB.
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Turnbull sells Snowy Hydro storage plan amid party divisions
Mr Turnbull, who hails from the moderate faction, sought on Wednesday to declared himself a champion of conservative issues.
"There is nothing more conservative than ensuring you have affordable and reliable electricity," he said at the Snowy Hydro plant at Cooma.
Mr Pyne said in his statement the Liberal Party had long been "the crucible of both liberal and conservative thought and values".
Energy Minister Josh Frydenberg said differences should be kept inside the party room, rather than aired publicly.
