Mike Dailly, a prominent campaigner for a No vote in the independence referen-dum, used abusive language to describe Alex Salmond on social media site Twitter.
The rant on Saturday evening prompted angry responses from both Yes and No supporters, including Transport Minister Keith Brown MSP, chairman of the Scottish Labour Party Jamie Glackin and Scottish Greens co-convener Patrick Harvie.
Mr Dailly is principal solicitor at Govan Law Centre and sits on the board of the Scottish Housing Regulator, an independent body that reports to the Scottish Parliament.
The lawyer claims its chairwoman Kay Blair called him yesterday to demand his resignation.
Mr Dailly said: "She asked if I was going to resign. I asked why and she said it's because of my tweet. I said no, I have no intention of resigning.
"We have Article 10 of the European Convention on Human Rights for a reason. It provides the right to freedom of expression, but it would seem if you attack the First Minister you get sacked."
The former Scottish Solicitor of the Year also questioned why he should be forced out when the First Minister's adviser Campbell Gunn kept his job despite a recent row over an email he sent to a newspaper.
Mr Dailly was appointed to the £8000-a-year part-time post in March last year.
The media was informed at the time that Mr Dailly is a member of the Labour Party but that political activity plays no part in the selection process, which is regulated by the Public Appointments Comm-issioner for Scotland.
Mr Dailly has written to Ms Blair to underscore he intends to stay on the board.
Ms Blair told the Evening Times: "It is not my place to ask any board member to resign. You'd have to speak to the housing minister."
A Scottish Government spokeswoman said: "Any concerns about this matter should be put to the Government in writing."