Martin McGuinness has said he believes the INLA could have done a more dignified job of honouring veteran republican Peggy O'Hara at her funeral.
As the former IRA commander criticised the paramilitary displays of today, he also ruled out Sinn Fein taking seats at Westminster - even to prop up a future left wing Labour government which needed support.
The Deputy First Minister was commenting on the possibility of Jeremy Corbyn - a long term supporter of Irish unity who has said the government should give Northern Ireland more financial help with welfare - becoming prime minister.
In a wide-ranging interview for the Belfast Telegraph, Mr McGuinness also denied relations with Peter Robinson were bad and suggested they may broker a solution to the budgetary problems in the autumn.
But he was highly critical of INLA after masked and uniformed men and women marched in formation through Londonderry at the funeral of Peggy O'Hara. The republican matriarch was the mother of INLA member Patsy O'Hara, who died on hunger strike in the Maze Prison in 1981.
Mr McGuinness said: "The sight of people in masks marching in the numbers that they marched in in the streets of Derry was more about their agenda than about honouring Peggy O'Hara.
"What is the point in it? The people who were marching at Peggy O'Hara's funeral gave the impression they were associated with the INLA which is supposed to be on ceasefire and to have decommissioned some of their weapons. I ask if they could have honoured her in a more dignified way."
Since its foundation Sinn Fein has abstained from taking any seats it won in Westminster because it does not recognise the right of Britain to rule any part of Ireland. Asked about ending the policy Mr McGuinness said: "No. Our position has been on the record for many decades and I don't envisage any change whatsoever; there is no mood for it within the party. Quite apart from the principle involved it could damage the cohesion of mainstream republicanism." On Mr Corbyn he said: "A lot of Labour people are telling me Labour is in poor shape. Given that Jeremy has been a very good friend for us for many years we obviously wish him well."
Mr McGuinness said the perception that the relationship between himself and First Minister Peter Robinson was fraught was misinformed.
"There are colleagues of yours in the media, who use phrases like 'they hate one another'," he said.
"I don't hate Peter Robinson and I don't think Peter Robinson hates me. We have worked together in the Office of the First Minister and Deputy First Minister since 2008. If relationships were as bad as they are portrayed, then I don't think the institutions could have survived so long.