Suella Braverman has accused Gary Lineker of diminishing the Holocaust as ministers engaged in an open row with the BBC presenter over his criticism of their asylum plans.
The former England striker likened the language used to launch the new Conservative policy to that of Nazi Germany.
The home secretary said she found his comments “offensive” because her husband is Jewish.
“My children are therefore directly descendant from people who were murdered in gas chambers during the Holocaust,” she told the BBC’s Political Thinking podcast.
“To kind of throw out those kind of flippant analogies diminishes the unspeakable tragedy that millions of people went through and I don’t think anything that is happening in the UK today can come close to what happened in the Holocaust.
“So I find it a lazy and unhelpful comparison to make.”
Lineker suggested he will avoid suspension by the BBC for his comments.
The BBC has said it is taking the matter “seriously” and expects to have a “frank conversation” with the presenter, who confirmed he had spoken to director-general Tim Davie.
Lineker tweeted: “Well, it’s been an interesting couple of days. Happy that this ridiculously out of proportion story seems to be abating and very much looking forward to presenting @BBCMOTD on Saturday.”
He told reporters outside his London home that he stands by his criticism of the immigration policy and does not fear suspension.
Criticism also came from culture secretary Lucy Frazer, who told the Commons it is important for the BBC to maintain impartiality if it is to “retain the trust of the public who pay the licence fee”.
Gregory Campbell, DUP MP for East Londonderry, called for “lefty Lineker” to face a salary reduction.
Last year the former England footballer was named as the BBC’s top earning on-air talent for the fifth consecutive year, and was paid between £1,350,000 and £1,354,999 in 2021/2022 for Match Of The Day and Sports Personality Of The Year.
However, support has come from media figures including Piers Morgan and Sky News commentator Adam Boulton, who said he thought Lineker was “entitled to say what he likes” on Twitter because he is not a political reporter.
Mr Davie previously warned staff about their use of social media when he took on the role at the end of 2020, and guidelines around social media use have since been updated.
Staff were told they need to follow editorial guidelines and editorial oversight in the same way as when doing BBC content.
Lineker is a freelance broadcaster for the BBC, not a permanent member of staff, and is not responsible for news or political content so does not need to adhere to the same rules on impartiality.
He responded on Twitter to a Home Office video in which Ms Braverman unveiled plans to stop migrants crossing the Channel on small boats.
The ex-England striker wrote: “There is no huge influx. We take far fewer refugees than other major European countries.
“This is just an immeasurably cruel policy directed at the most vulnerable people in language that is not dissimilar to that used by Germany in the ’30s.”