The row between Immigration Minister James Brokenshire and Cable erupted as an official government study concluded there was "relatively little evidence" that migrant workers had taken the jobs of Britons when the economy was strong.
The review said there was evidence of "some labour market displacement" during the recession.
But it also found there was little evidence that immigrants from the European Union had an impact on the employment of British workers, although it was a "relatively recent phenomenon" and "this does not imply that impacts do not occur in some circumstances".
Brokenshire, making his first speech as immigration minister, attacked Cable's views and said the number of recent arrivals from the European Union was "just too high".
"Mass immigration puts pressure on social cohesion, on public services and infrastructure and -- yes -- it can force down wages and displace local people from the job market," he said.
"The winners are the haves like Vince, but the people who lose out are from working class families, they're ethnic minorities and recent immigrants themselves."
Conservative ministers have frequently cited research from 2012 by the Migration Advisory Committee (MAC) covering the period from 1995 to 2010 that found 23 British workers were left unemployed for every 100 new arrivals from outside the EU.
But the new analysis stated that when data from the recession years of 2009 and 2010 was omitted, the impact of non-EU migration was not "statistically significant".
Brokenshire's predecessor as immigration minister, Mark Harper, was forced to resign after he discovered his cleaner did not have permission to work in Britain.
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