According to government figures, just over 370,000 people claiming benefits are migrants who came to the UK as foreign nationals.
Employment minister Chris Grayling told the Today programme's John Humphrys that of the 370,000 names in the data, roughly three quarters had been identified and "most are legitimate".
Releasing the figures was not "scaremongering", he insisted, but that it is "important to have a benefit system in which people can have confidence".
"Maybe there isn't a problem right now", he said, but said he wanted to tighten the rules so that we don't have a country in which "benefit tourism" is an issue.
Get in touch with Today via
or text us on 84844.