Lord Forsyth of Drumlean criticised the SNP leader over her party’s “antics” towards the withdrawal from the EU, with threats of a second independence referendum.
Given the problems north of the border, including rising unemployment, the Tory peer suggested Ms Sturgeon “sticks to her day job” and “doesn’t get involved in foreign affairs”.
Lord Forsyth was speaking during a debate in the House of Lords on the impact of the UK’s split from Brussels, including the status of EU citizens living in Britain and Britons living in the EU.
The peer said: “One thing that the Liberals and the SNP have in common is that they are crying out for more referendums, but at the same time won’t accept the result of referendums when people actually vote.
“I suggest to the First Minister that she sticks to her day job and concentrates on unemployment and the problems in the health service and the problems in education and the problems elsewhere, and perhaps doesn’t get involved in foreign affairs.”
Lord Forsyth pointed out the SNP had made Donald Trump a business ambassador for Scotland “and promptly withdrew it whilst calling on the Government to ban him from coming into this country”.
“I suggest her expertise may not lie in that area and she should butt out of this particular debate.”
Lord Forsyth agreed the need to reach a swift resolution over the position of EU citizens living in the UK.
“The way to resolve it quickly is to get on with moving Article 50 and persuading our colleagues in the European Union that we need a reciprocal deal. That those British people living in the European Union are able to stay in the European Union and likewise people who have come here will be able to stay.
“Nobody seriously thinks that more than three million people are going to be expelled from this country.”
He said it was “irresponsible to create fears and anxieties amongst those people”.
Opening the debate, opposition spokesman Baroness Hayter of Kentish Town had highlighted the “great anxiety” felt among EU nationals living in the UK.
“We must resolve the legal status of these citizens without delay,” she said.
“The people have indeed spoken about Brexit, but Brexit needs to think about people.
“It needs to be managed in a way that safeguards individuals’ rights and a way that helps our economy to prosper and grow for the sake of all our people.”
Labour peer Viscount Chandos urged the Government “to take the lead by unilaterally guaranteeing the rights of EU citizens currently residing in the UK”.
“It is neither morally nor economically attractive to attempt to use their position as a negotiating ploy, nor do I believe it is even a good negotiating tactic.”
The Bishop of Durham, the Rt Rev Paul Butler, highlighted “continuing uncertainty hanging over families”.
He said: “This uncertainty and the resultant stress and strain on family life and children should not have a place in our negotiating strategy.
“It does not speak to the type of Brexit we should aspire to.”