It was wrong for the European Court of Human Rights to intervene with the plan to take asylum seekers from the UK to Rwanda, Dominic Raab has said.
The deputy prime minister said the flight's grounding strengthened the case for reforming human rights laws.
The first flight of the Rwanda asylum plan, scheduled for Tuesday evening, was halted after the court intervened.
Plans for future flights have begun and the government remains committed to the plan, Priti Patel told MPs.
"We will not be deterred from doing the right thing," the home secretary said on Wednesday.
The Rwanda asylum plan, announced by the government in April, intends to take some asylum seekers who cross the Channel to the UK on a one-way ticket to Rwanda to claim asylum there instead. The government has said the scheme would discourage others from crossing the Channel.
Up to seven people had been expected to be removed to Rwanda on the Boeing 767 on Tuesday evening - which was halted minutes before take-off.
But despite clearing UK courts, the flight was halted by a late intervention from the European Court of Human Rights (ECHR) which led to fresh challenges in the UK courts.
Refugee organisations, politicians and the Church of England are among those who have criticised the asylum plan.
Charities and lawyers representing asylum seekers have also launched a series of legal challenges against the policy.
Justice Secretary Mr Raab said it had been "quite wrong" for the Strasburg court to use a special power to block the removal of some of the asylum seekers.
It had turned to a little-used court rule, that is technically not part of the core law of the European Convention on Human Rights - the treaty the UK is part of.
He said that the court's ability to use this injunction power would end under his planned reforms.
The UK's High Court was "very clear" and said there was "no realistic risk that in the interim period there would have been any harm to those who would have been deported", the deputy prime minister said.
The High Court ruling also accepted there was a "material public interest" in the home secretary being able to carry out her policies.
Asked if the UK could simply ignore the European court's ruling, Mr Raab said: "Not under the Human Rights Act, but we will address this squarely with the bill of rights."
The bill of rights is a plan by the government that would see changes made to the Human Rights Act. Under the plan, the UK would stay party to the European Convention on Human Rights but would change how it is interpreted by courts.
Mr Raab said the grounding of the flight "does strengthen" the case for reform.
"We're going to stay in the convention but make sure the procedural framework is reformed", he told BBC Radio 4's Today programme.
The changes would "stop and change the ability of the Strasbourg court to issue what amounts to effective injunctions when they have no power grounded in the European convention to do so", he said.
But speaking to the BBC's Radio 4 PM programme, Home Office minister Tom Pursglove said: "My understanding is that we would be able to do that [leave the European Court of Human Rights] if we wanted to."
Mr Pursglove added he had not seen the court's judgement and would not make "pre-emptive commentary" about what they do after.
"We then need to decide what interventions we need to make to make sure that this policy is enacted because the British people want us to stop these crossings of the Channel and get on and do the job," he said.
Warm weather and low winds provided ideal conditions for crossing the English Channel on Wednesday when 233 migrants were brought to shore, the government said. On Tuesday, 444 migrants tried to cross the English Channel in small boats, the highest number in a single day for two months.
What is the European Court of Human Rights?
The ECHR is an international court that sits in Strasbourg in France and protects civil and political rights.
These rights were established in a treaty called the European Convention on Human Rights, drawn up in the aftermath of World War Two - largely written by British civil servants and lawyers.
The convention has nothing to do with the EU - so the UK remains part of it despite Brexit.
The British government is bound by ECHR rulings, including the injunction that prevented a passenger from boarding a flight to Rwanda.
The ECHR should not to be confused with the European Court of Justice - which is a separate court that settles disputes between EU members.
It's extremely rare for a country to withdraw from the ECHR's jurisdiction. Russia was expelled following its invasion of Ukraine, Greece temporarily left following a military coup, while Belarus is not part of the Convention.
Two asylum seekers who were expected to board the flight have told an Iranian human rights lawyer they were treated like criminals and described one man being taken to the plane in a wheelchair after passing out.
Shadi Sadr, of Justice for Iran, told the BBC the pair said they had been held in separate vans at the airport, each with three guards.
One said they had been handcuffed, the other that their hand had been tied to a seat in the van, she said.
"They were already traumatised by their journeys here and the uncertainties of what was happening to them - it's an inhuman way to treat people," she told the BBC.
Mitie, the facilities management company which runs immigration centres and was escorting the asylum seekers to the plane, said that restraint was only used as a last resort, to ensure the safety of both those travelling and its staff members.
"This includes the prevention of injury or self-harm," its statement added. "Our focus is on treating the people in our care with dignity and respect, and we are confident that our officers have acted professionally."
Speaking in the Commons on Wednesday, the home secretary defended the policy and said the court ruling was "disappointing and surprising".
She said: "Preparations for our future flights and the next flights have already begun."
"We will not stand idly by and let organised crime gangs, who are despicable in their nature and their conduct, evil people, treat human beings as cargo."
Labour's Yvette Cooper called the policy a "shambles" and "shameful".
The government knew there were "torture and trafficking victims" among those the government planned to put on the plane, the shadow home secretary told MPs.