David Cameron is under pressure to stop hiding an official report which would undermine government rhetoric about immigrants pushing British workers out of their jobs.
This comes just weeks after the government came under pressure to publish a different report suggesting that EU migration was good for Britain, amid fears that it could be politically awkward in the run-up to the European Elections.
Ministers including home secretary Theresa May have repeatedly quoted research by the Migration Advisory Committee that found that 23 British workers are left unemployed for every 100 new arrivals.
However, a study by civil servants concluded last year that the "displacement" figure is significantly lower, BBC's Newsnight programme reported.
Ministers are believed to be suppressing the report amid concerns that it could be politically uncomfortable.
Liberal Democrat MP Julian Huppert, member of the Home affairs select committee, told Newsnight: "It's obvious that this report should be published as quickly as possible.
"We have to have the right figures, so we can make the right decisions, so that we get the best people here to help our economy."
Shadow immigration minister David Hanson said: "The British people should have information made available to them so they can make a judgement about the impact of immigration on jobs.
"This should be done on the basis of fact, not more empty rhetoric or spin from the Government."
UK Independence Party leader Nigel Farage told BBC Radio 4's Today programme: "I think there is no doubt that British people have lost their jobs because there is too much labour coming into the market.
"The other factor, which is not in this report but is perhaps even more pertinent, is the effect on wages of people in work.
"We have had wage compression and it has meant lower wages for millions and millions of people."
Liberal Democrat MP Martin Horwood joined calls for a swift publication: "Let's put it kindly: it's got stuck in someone's in-tray waiting for the final sign-off, hasn't it?
"It would be very, very helpful if it was now extracted from that in-tray and published.
"It sounds as though this is a very rigorous study ... a very important contribution to the factual debate on immigration which is sorely needed."