The chairman of the Conservative Muslim Forum has told the BBC he will resign his party membership if Boris Johnson wins the leadership race.
Mohammed Amin said the MP was not “sufficiently moral” to be PM.
He criticised Mr Johnson’s comments about burkas and his denial that he had mentioned potential Turkish membership of the EU when campaigning for Brexit.
But MP Priti Patel defended Mr Johnson, who had apologised for any offence caused and had defended women’s rights.
Mr Johnson topped the poll of 10 candidates running to replace Theresa May as party leader and prime minister on Thursday, winning 114 votes – more than a third of all Tory MPs. This more than twice the support for his nearest rival, Foreign Secretary Jeremy Hunt, who received 43 votes.
The remaining six candidates – following Health Secretary Matt Hancock’s withdrawal on Friday – will face another ballot on Tuesday in which they will need to secure 33 votes to stay in the race.
Mr Amin told BBC Radio 4’s Today programme: “I have been a Conservative Party member for over 36 years. We don’t expect our politicians, our prime ministers, to be saints but we do require a basic level of morality and integrity.
“And of all of the candidates in the Conservative Party leadership election, Boris Johnson is the only one that I believe fails that test. And I’m not prepared to be a member of a party that chooses him as its leader.”
He said Mr Johnson had chosen “to mock Muslim women who wear [the] niqab and burka for his own purposes” and had “denied point blank that he had ever said that Turkey was joining the European Union”.
Ballots will continue until the list is whittled down to two leadership contenders, who will then go to a party-wide vote.
When it was put to him that Mr Johnson was popular with MPs and party members, Mr Amin said: “A lot Germans thought that Hitler was the right man for them.”
He added: “As far as I am concerned, [Mr Johnson] has insufficient concern about the nature of truth for me to ever be a member of a party that he leads.”
In a Daily Telegraph article in August 2018, Mr Johnson said full-face veils should not be banned, but it was “absolutely ridiculous” women chose to “go around looking like letter boxes”. He also compared them to looking like “bank robbers”.
Former cabinet minister Priti Patel, who is backing Mr Johnson’s leadership bid, said she “took issues with some of the points that were being made” in the interview with Mr Amin and said the Telegraph article had been “a defence of women’s right to wear whatever they like”.
She said he had apologised for any offence caused but “he was certainly not mocking women in the way in which was asserted”.
“Language can be misused, taken out of context. But Boris himself .. he believes in equality of the sexes.”
Asked about the comments about Mr Johnson’s morality, she said: “That’s a very sharp and harsh position to take.
“That article was Boris’s very clear defence of women’s rights to wear whatever they like, it was not written to mock in the way which was asserted in the interview earlier on.”
MP Andrew Bridgen, who is also backing Mr Johnson, said: “I’m deeply disappointed that anyone would want to leave the Conservative Party. There’s nothing more divisive than a Conservative Party leadership election.”
He added: “I’m sure there are unfortunately other people who wouldn’t want to be in the party if other people became the leader.
“Brexit is a very divisive issue. I don’t think we can bring the party together at all until Brexit is dealt with and we’ve actually left. Boris is I think the person to deliver Brexit – he believes in Brexit and he’s a proven winner.”
The Conservative Muslim Forum was founded by Tory peer Lord Sheikh in 2005 and aims to encourage Muslims to participate in politics and support the party.