Priti Patel has suggested it is "simply not right" for people to arrive in the UK with all their correct documents, and then claim asylum.
The Home Secretary suggested "genuine" seekers fleeing dangerous situations would arrive on Britain's shores without anything to hand.
But those who arrive without any documents would have access to temporary permission to stay in the UK, a committee heard.
Lord Blunkett asked the Home Secretary how she would clamp down on organised crime, particularly in the form of human trafficking.
Ahead of the Budget statement, Ms Patel told the Lords Justice and Home Affairs Committee she recognises the need to give support to "people who are fleeing persecution and we recognise that they are undocumented".
Lord Blunkett asked the Home Secretary to detail how someone can claim asylum if they have a passport, a visa or managed to come via a legitimate route from their country.
He added: "How do they claim that they are persecuted in those circumstances? When we all know that the people who are persecuted are often the ones who are without documentation, without the passport without the permission of their country to leave?"
Ms Patel responded: "Well, I think on this point, I mean, those that are documented... they cannot... I mean, you've already mentioned, if they've got visas, if they've got legal documentation, that is simply I mean... we have clear processes around asylum.
"Our focus has to be on those that we want to give support to we need to give support to, [people] who are fleeing persecution, who are undocumented, we recognise that they are undocumented, but it is through - and you'll be familiar with many of the previous asylum processes [and] how we now change our interview processes - how we effectively ensure that we are granting asylum to those that are genuine asylum seekers.
"Not those who turn up at primary control points, at our airports and basically then effectively require special case working through Border Force to say, here I am with all my documentation, and I'm here seeking asylum. That is simply not right."
Lord Blunkett attempted to seek further clarification as he said: "I get the impression that if you are properly documented, and you've been able to come (to the UK) in your terms, Secretary, legally, you'll not be granted asylum because you're clearly not at risk."
But the Committee - under time constraints ahead of the Budget statement - were swift to move on.
Baroness Chakrabarti later slammed Ms Patel's announcements earlier in the year, to clampdown on immigrants who arrived on English shores.
She told the Home Secretary "any attempt to turn around little boats full of desperate people in the English Channel is pretty shocking. And it's almost the opposite of the Dunkirk spirit".
A Home Office spokesperson said: “Our New Plan for Immigration will prioritise protection for the most vulnerable individuals fleeing persecution through safe and legal routes.
“If someone has travelled via a safe country like France, then their claim may be considered ‘inadmissible’ and they could be removed from the UK.”
It comes as Ms Patel seeks to get her nationality and borders bill through Parliament.
The controversial bill would give the government the power to use “scientifically verifiable” measurements of bones or take DNA samples to check the age of people who are seeking to live in the UK.
Ms Patel faced heavy criticism earlier this year rubbishing the experiences of migrants in the Commons as she claimed “genuine people are being elbowed aside” by those paying traffickers to come to the UK.
Ms Patel said the principle of seeking refuge had been “undermined” by people who come to the UK by choice, not because it's the safest country closest to them.
The Home Office previously said the bill will "prioritise those most in need of protection while stopping the abuse of the system".
