Tony Blair insisted on Tuesday that the Northern Ireland peace process could have collapsed if he had not allowed letters to be sent to suspected IRA fugitives telling them that they were no longer wanted by the police.

During intense cross-questioning by MPs at Westminster, the former prime minister said the “on-the-runs” issue was an “essential component” of keeping the republican party, Sinn Féin, in the negotiations, although he accepted there had been mistakes in administering it. “Without dealing with this issue, we would not have had a Northern Ireland peace process,” he said.

The scheme – which was set up in 1999 after the 1998 Good Friday agreement – involved sending letters to more than 200 republican paramilitary suspects, on whom there was deemed not to be enough evidence to form a prosecution, and informing them that they were no longer wanted by the police. According to the agreement, those convicted of paramilitary crimes became eligible for release, but this did not cover those suspected of paramilitary crimes or those who had been charged and had subsequently escaped, known as on-the-runs.

Blair told the Northern Ireland affairs committee he agreed completely with the assessment made by Lady Justice Hallett in an inquiry into the scheme published in July last year. Hallett concluded that the on-the-runs scheme was lawful and did not give terror suspects an amnesty, but that the scheme had not been properly administered.

Prosecution of John Downey, charged with carrying out the 1982 IRA Hyde Park bombing that killed four soldiers, collapsed earlier in 2014 when it was discovered that he had been sent a letter of reassurance that he would not be prosecuted. Blair admitted that he hadn’t even heard of Downey until the case came to court.

Blair described the sending of a letter to Downey as a mistake that he took full responsibility for because of his position as prime minister at the time and apologised to people who had been affected by the error. “I am sorry for those people and I apologise to those people who have suffered as a result of that,” he said. “But I am not going to apologise for sending those letters to those who should have received those letters, because without having done that, we would not have a Northern Ireland peace process.”

Blair disputed the idea that the letters had been sent out in secret, pointing to times when questions had been asked about the letters in parliament and had been answered openly. But he said he was not in a position to dispute accounts by David Trimble, former first minister of Northern Ireland and leader of the Ulster Unionist party and other senior figures who say they didn’t know about the letters.

Blair said the letters were issued “so we could say we were doing something” about demands for a wider fugitive deal. Without the move, the whole process could have collapsed, he said.

“It was on a knife edge. I actually thought for a time during that period we’d lost the whole thing … if we hadn’t managed to find a way to get ourselves over what was a horribly difficult period, we would not have got the [Northern Ireland power-sharing] executive up in May 2007.”

Last September the the Northern Ireland secretary Theresa Villiers said that the government was no longer standing by the letters and that they should no longer be relied on as a defence. When asked what he would say to the current government, Blair said: “You inherited a peace process that worked, but be careful with it. It’s fragile still.”

Blair had previously declined to give evidence to the committee saying he was too busy, despite receiving two letters and several emails from the committee inviting him to do so. Blair finally agreed to give evidence after a phone call from the speaker of the Commons John Bercow last week in which he told Blair that parliament would take an extremely dim view of his refusal to give evidence.

Ann Travers, whose 22-year-old sister Mary was shot dead by the IRA coming out of a Roman Catholic church in 1984, welcomed Blair’s decision to give evidence to the inquiry. Her late father Tom, a magistrate in Belfast, had been the intended target of the IRA attack. He was badly injured in the shooting in south Belfast.

But she said: “However, I found some of his evidence disturbing. This scheme meant that some families would never get justice and to that end peace of mind … He [Blair] allowed himself to be blackmailed by Sinn Féin in order for us all to have the right to work and live our lives in peace.”Travers added: “Many victims feel disturbed because they feel that their rights as innocent victims have been put below Sinn Féin and the IRA, many now want complete transparency and won’t except the excuse of secret deals ‘for their own good’. They aren’t willing to be patronised or sacrificed any longer.”