The Conservatives could set out their stalls on a campaign to leave the European Convention on Human Rights (ECHR) at the next election if Rwanda flights continue to be blocked.
Robert Jenrick said the Government will do “whatever is required” to curtail the crossing of small boats across the English Channel.
But with the plan to send migrants to Rwanda still facing a Supreme Court battle, there is pressure within the Conservative Party to pull out of the ECHR to make it easier to address the situation.
Home Secretary Suella Braverman has previously expressed her personal view that the UK should leave the convention, which is ruled on by the European Court of Human Rights in Strasbourg.
The ECHR is a Council of Europe convention, rather than a European Union one, so the UK’s adherence to it was not affected by Brexit.
But pulling out of the convention would put the UK at odds with the majority of European nations and could also cause complications over the operation of the Good Friday Agreement in Northern Ireland and post-Brexit deals with the EU.
On Times Radio, Mr Jenrick would not rule out withdrawal from the convention, saying the Government will do “whatever is necessary”.
“You can see from the Prime Minister, the Home Secretary and myself, our total commitment to this challenge,” he said.
“That’s why we’re working on every possible front. That’s why we have produced the most comprehensive plan, I believe, of any European country to tackle this issue.
“And we’ll do whatever is necessary ultimately to defend our borders and to bring order to our asylum system.”
Pressed directly on whether that could include leaving the ECHR, he said: “We will do whatever is required, take whatever necessary action is needed.”
Mr Jenrick also warned asylum seekers in the UK that they cannot expect an “a la carte” selection of accommodation options after some launched challenges to avoid being placed on board the Bibby Stockholm barge in Portland, Dorset.
He told BBC Radio 4’s Today programme: “The way that the asylum support system operates is that if someone claims to be destitute – i.e. they have no way of supporting themselves – there’s a legal obligation on the Government to step in and provide them with accommodation and meet their basic needs, but we do that by and large on a no-choice basis, not an a la carte menu where you can choose which hotel you want or which location.
“And so, if you decline the accommodation that’s provided, such as the barge, then we will consider removing your asylum support, and that individual would then ultimately have to fend for themselves.”
He added: “We’re not making anybody destitute. They would be choosing to do so because they wouldn’t accept the perfectly decent accommodation.”