Immigration Minister Peter Dutton has delivered a blunt and public warning to Prime Minister Malcolm Turnbull not to waver on same-sex marriage, insisting the government "won't be bullied" and telling the country's business leaders to "stick to their knitting".

Meanwhile, Liberal MPs who wanted to bring same-sex marriage to a head in the next fortnight of Parliament say their plans have hit a wall, and now concede movement on the issue is unlikely in this half of the year.

Immigration Minister Peter Dutton warned the Turnbull government was "not going to be bullied" by chief executives "or anyone else". Credit:Andrew Meares

The letter from 20 of the country's chief executives calling on the Turnbull government to legislate for same-sex marriage appears to have backfired, with moderate Liberal MPs labelling it "unhelpful".

In the third successive day of his crusade, Mr Dutton lashed out at social media activists who were "blackmailing" companies by threatening boycotts, and warned the government would not abandon its policy of holding a plebiscite.