Health Secretary Matt Hancock has been accused of "whitesplaining" by Tory peer Sayeeda Warsi after he said others in the party took a "more balanced approach" on Islamophobia than her.
Baroness Warsi has repeatedly criticised the party's response to Islamophobia in its own ranks.
On Friday, Boris Johnson appeared to rule out an independent inquiry specifically into Islamophobia.
He said the party would hold a "general investigation into prejudice".
Speaking to BBC Radio 4's Today programme on Saturday, Mr Hancock said the Tories needed to hold an inquiry on Islamophobia within the party.
But he added: "Well look, I like Sayeeda [Warsi], she has a particular view on this. There are others who take a more balanced approach," he said.
Asked if he was saying she was "unbalanced", Mr Hancock replied: "No, I'm certainly not saying that. I have an enormous amount of respect for Sayeeda but she does take a particular view."
He added: "There needs to be an inquiry of course but, of course, you should look into all kinds of prejudice.
"I think that this is something that any responsible party always needs to be on the look-out for."
Baroness Warsi, the UK's first female Muslim cabinet minister, responded with a tweet saying she was "glad" to have colleagues like the health secretary to educate her on the issue after working in race relations for 30 years.
"Thousand apologies sir," the former Tory chairwoman added.
The Conservative Party has come under pressure to open itself up to an independent inquiry into Islamophobia following incidents highlighted to the party and in the media.
In September, a number of party members were suspended after the BBC highlighted more than 20 cases of Islamophobic material being posted or endorsed online.
The incidents ranged from individuals "liking" anti-Muslim pictures or statements on one or two occasions, to regular Islamophobic posts by people who said they were members of the Conservative Party.
Oh @MattHancock— Sayeeda Warsi (@SayeedaWarsi) November 9, 2019
Thank you for “whitesplaining” this to me.
I’m so glad I have colleagues like you who can educate me even after my 30 years of experience of work in Race relations
“”Thousand apologies sir “ 🙄🤦🏽♀️ https://t.co/7TtX34PHT8
On one occasion, a Conservative councillor responded to a tweet in March, writing: "Islam and slavery are partners in crime."
Speaking to Channel 4 News on Saturday evening, Baroness Warsi said Mr Johnson's comments suggesting a broader investigation showed the party was still not taking the issue of Islamophobia seriously.
She called for him to be an "anti-racist" and "take all forms of racism seriously".
"We've quite rightly been calling out the Labour Party for the allegations of racism within their ranks... we seem to be able to take our opponents to task, and yet we singularly fail to deal with the Islamophobia and racism in our own backyard," she said.
Asked whether she could urge her fellow British Muslims to vote Conservative, Baroness Warsi said: "I would say that the climate for British Muslims within the Conservative Party is hostile.
"I think that the climate that has been created in the country because of the Conservative leadership is hostile for British Muslims."
In June, during a BBC debate as part of the Tory leadership contest, candidate Sajid Javid, now the chancellor, asked other candidates to agree to open up the Conservatives to an external investigation into Islamophobia within its ranks.
Mr Johnson nodded in response.
2/2 Today #BorisJohnson has confirmed that there will NOT be an inquiry into #Islamophobia— Sayeeda Warsi (@SayeedaWarsi) November 8, 2019
Yes it’s true my party don’t give a —— about racism within our own ranks
We are only anti racist to score political points
Do as we say not as we do 🤦🏽♀️
On Tuesday, cabinet minister Michael Gove told the Today programme the party would "absolutely" hold an independent inquiry into Islamophobia before the end of the year.
But in an interview with BBC Radio Nottingham on Friday, the prime minister said the party would investigate "prejudice of all kinds".
In response, Baroness Warsi tweeted: "Today #BorisJohnson has confirmed that there will NOT be an inquiry into #Islamophobia. Yes disappointing. Yes predictable."