An extraordinary public row between the home secretary, Shabana Mahmood, and one of her junior ministers has escalated after he said he “won’t be intimidated” in response to calls by her for him to be sacked.

Mahmood demanded on Thursday that the migration minister, Mike Tapp, should be fired for writing an unauthorised article in the Times calling for overseas care workers to be exempt from controversial changes to the immigration rules. But Keir Starmer has so far not sacked Tapp for apparently breaking the rules around ministerial conduct.

In the most visible evidence of a breakdown of discipline in the last days Starmer’s time in charge of government, Tapp used his X account to deliver a defiant response. He wrote: “Ok, morning all. It’s gone from ‘he broke the ministerial code’ to ‘he stole my idea’.

“I have put my views across on a policy I’ve been working on for months (I have the receipts) in an Op Ed in the times. Give it a read, and let’s continue to discuss.”

Above a picture of himself, he added: “I won’t be intimidated to drop my views. Stay classy! Oh and I’m at a wedding in San Francisco, but happy to talk more when I’m back (I promise that’s the Golden Gate Bridge hidden by the fog).”

No 10 has so far refused to officially sack Tapp, saying on Thursday that “no decision” had been made by the prime minister. However, pressure was building on Friday as another member of the government said it was “unwise” for junior ministers to set out views in the way Tapp had done.

The row comes as senior Labour figures tussle for leading roles in Andy Burnham’s prospective administration, which is expected to take power in No 10 as early as 17 July.

Tapp wrote in the article for the Times that it was his “strong belief” that migrant care workers should not have to wait longer to apply for permanent settlement in the UK.

Mahmood was unaware he had written the article, which a source close to her insisted was done “to try to win a job in the new administration”.

It is understood Tapp was involved in ministerial discussions about exempting care workers from the proposed changes to indefinite leave to remain. It is alleged he took an idea proposed in those discussions and attempted to pass it off as his own in the Times article.

The justice minister Jake Richards told Times Radio the Home Office needed to “take a deep breath”.

“Mike’s article in the Times sets out what his views are and some of the issues that he in the Home Office is exploring,” he said. “It’s not particularly wise in my mind for junior ministers to kind of set that out publicly. We are part of a team, but he has done that and we will deal with that as a government.”