LONDON – IRA commander-turned-political peacemaker Martin McGuinness said Thursday that he regrets “every single life” lost in Northern Ireland’s decades of violence, and he expressed hope that his handshake with Queen Elizabeth II would be a key building block in a new relationship between Britain and Ireland.

McGuinness, who is the deputy leader of Northern Ireland’s Catholic-Protestant power-sharing administration, said his historic meeting Wednesday with the British monarch was meant to offer “the hand of friendship” to Protestants who were once his enemies.

“It was a meeting which, although short in length, I believe can have much longer effects on defining a new relationship between Britain and Ireland and between the Irish people themselves,” McGuinness said in a speech to supporters at the Houses of Parliament in London.

McGuinness is an elected British lawmaker, but like other members of his Irish nationalist Sinn Fein party, he refuses to take his seat in the House of Commons. McGuiness said he would quit as a member of Parliament to focus on his duties in Northern Ireland, though he did not say when he planned to leave.

In an otherwise upbeat speech, McGuinness accused the British government of hampering further reconciliation in Northern Ireland with “wrong and unhelpful” decisions. He said Britain had failed to “acknowledge its role as a combatant in the conflict” that killed about 3,700 people over the past four decades.

The Provisional Irish Republican Army, which McGuinness once led, was responsible for some 1,775 of those deaths; British soldiers killed 309 people.

McGuinness accused Prime Minister David Cameron of a “lack of engagement” and of failing to tackle issues that anger Irish nationalists, such as refusing to hold public inquiries into controversial killings of Irish republicans.