Suella Braverman has turned down an invite from Archbishop Justin Welby to discuss the Government's position on migration.
Welby is said to have reached out "a number of times" without success.
The Archbishop has been a vocal critic of the Government's approach to immigration, expressing concern about the Home Office's "harmful rhetoric".
A spokesperson for the Archbishop said: "The Archbishop would be happy to meet the Home Secretary to discuss issues of mutual interest and concern.
WATCH NOW: Suella Braverman calls for world leaders to rip up UN Refugee Convention
"In the past, the Archbishop has met other home secretaries. It is not unusual."
A former adviser to the bishops who sit in the House of Lords told The House magazine that Braverman's response was seen as a "big slap in the face" at Lambeth Palace.
They said it had caused "consternation" from the Church of England.
Government sources said an informal approach had been made but said the Archbishop had met with Immigration Minister Robert Jenrick.
In her latest intervention, Braverman suggested that anti-gay discrimination is not a qualification for seeking asylum in a speech calling for world leaders to crack down on migration.
She demanded world leaders rip up the UN Refugee Convention and instead introduce a migration regime "fit for our modern age".
Speaking in Washington in front of the centre-right thinktank American Enterprise Institute, Braverman said: "Seeking asylum and seeking better economic prospects are not the same thing."
The Home Secretary said "simply being gay, or a woman" should not by itself be enough to qualify for protection under international refugee laws.
She added: "Let me be clear, there are vast swathes of the world where it is extremely difficult to be gay, or to be a woman. Where individuals are being persecuted, it is right that we offer sanctuary.
"But we will not be able to sustain an asylum system if in effect simply being gay, or a woman, and fearful of discrimination in your country of origin is sufficient to qualify for protection."
The Home Secretary said that refugees cannot be allowed to "shop around" for safe havens, arguing that the convention is being interpreted as providing a right to asylum to those who face discrimination, rather than persecution.
In an interview with GB News' Lee Anderson, Braverman said a failure to "get a grip" on the migrant crisis will lead to a "disintegration" of our society.
She said: "Whether it is New York City, whether it is the border with Texas, whether it is Italy, whether it is the Channel, we need to look again at whether these international rules are fit for purpose.
The Archbishop has been a vocal critic of the Government's approach to immigration, expressing concern about the Home Office's "harmful rhetoric"
"And what I said in my speech is that there is a lot at stake. There is democratic legitimacy which is at stake.
"People want control of their borders and they want government to get a grip on this and if we don't it will lead to a disintegration in our society.
"And we need to change - we need to change some of the definitions relating to refugee persecution. It needs to be a high bar if someone is coming to our country fleeing persecution, not a low bar."and had been seen as a "big slap in the face" at Lambeth Palace.