UK companies will not be told to list or name foreign workers they employ, the government has said.
Defence Secretary Michael Fallon told the BBC: “This is not going to happen” but said firms could be asked “simply to report their numbers”.
Last week a Conservative briefing suggested firms would have to be “clear about the proportion of their workforce which is international”.
Labour’s Diane Abbott said the Tories were in “disarray” over their policy.
The proposal was mentioned in a briefing at the Conservative Party conference last week, where ministers gave more details on how the UK would respond to June’s referendum vote to leave the European Union – a key factor of which is believed to be concern at levels of EU immigration.
One of the critics of the proposal, Steve Hilton, an aide to former prime minister David Cameron, described it as “foreign working shaming”.
He addressed his thoughts to Home Secretary Amber Rudd in the Sunday Times: “Hey Amber, for your next brainwave, why not announce that foreign workers will have numbers tattooed on their forearms? You might as well do the job of killing Britain’s reputation as an open, enterprise economy properly.”
But Defence Secretary Mr Fallon told BBC Radio 5 live’s Pienaar’s Politics: “What I can absolutely rule out is that we will not be asking companies to list or publish or name or identify in any way the number of foreign workers they have.
“We’re going to consult with business, and the consultation document hasn’t even been published yet, on how we can do more encourage companies – to incentivise them – to look first at the British labour market. And to offer these jobs to British people, which is what the British people would expect, before they import labour more cheaply from abroad.”
He said businesses already had to go through a “resident labour market test” for non-EU workers but the government wanted to examine “whether we can get a better picture of exactly what the dependence on foreign workers is in each particular sector”.
“That would mean, for example, asking companies just simply to report their numbers, which we wouldn’t publish, we wouldn’t identify anybody.”
Asking companies to name foreign workers “would be, self evidently, a poor thing to do” and would cause “understandable concerns,” Mr Fallon said.
Education Secretary Justine Greening also told ITV’s Peston on Sunday the policy was “about collecting the right evidence if we are going to be able to respond to skills shortages… This is not data that will be published, there will be absolutely no naming and shaming”.
Labour’s new Shadow Home Secretary Diane Abbott said: “The Tories are in disarray following Amber Rudd’s worrying statement last week, contradicting each other as their policy falls apart at the seams.
“The Tories anti-foreigner agenda is a distraction from their own complete failures of policy, and against the best interests of society … We need answers from the Tories on how they will protect our economy, but they have no plan other than a risky hard Brexit which would threat our prosperity.”
Among business leaders criticising the idea last week was acting director general of the British Chambers of Commerce, Adam Marshall, who said: “It would be a sad day if having a global workforce was seen as a badge of shame”.
Scotland’s First Minister Nicola Sturgeon described it as “an appalling, regressive and hugely troubling development” while Lib Dem leader Tim Farron described it as “a nasty little policy”.
While Ms Rudd did not make the proposal in her speech to the Conservative Party conference, a briefing was sent around afterwards on proposals on how to make sure migrant workers were not doing jobs that could be done by British workers and “whether employers should have to… be clear about the proportion of their workforce which is international, as is the case in the US.”
Following criticism, Ms Rudd defended her proposals earlier in the week. She told the BBC that British businesses had a “responsibility to local employment and we’re asking them to join us on this journey so they don’t automatically go abroad”.
She denied the proposal was xenophobic and said it was just one of several schemes under consideration and “not something we’re definitely going to do”.
BBC political correspondent Tom Bateman said ministers would argue that Mr Fallon’s comments did not represent a U-turn, as the suggestion was not yet government policy but it was a “significant rowing back” on what had turned out to be a very controversial idea.