The leader of the Democratic Unionist Party, the Rev Ian Paisley, has called on his opposite number in the Ulster Unionist Party, Mr David Trimble, to resign.
Mr Paisley's comments come following Mr Trimble's declaration yesterday that he did not intend to resign his post.
Mr Paisley said if the Upper Bann MP had any sense, he would step down following recent defections from his party.
The North Antrim MP said: "If Mr Trimble has any sense, looking at the demise of many Official Unionist leaders, he should get out while the going is good."
Mr Paisley's son and DUP policing board member, Mr Ian Paisley Junior, described Mr Trimble as unionism's weakest link.
The North Antrim MLA said: "It is fair to say that David Trimble is the weakest link as far as unionism is concerned.
"If Anne Robinson was in judgment, I know what she would be saying to the weakest link.
"We're gracious enough not to say it to him but unionism cannot function in a viable fashion if it has a weak unionist leader."
Mr Paisley and his son were commenting after a meeting with Police Service of Northern Ireland Chief Constable Hugh Orde.
The DUP leader said they had discussed the police investigation into concerns about a police front. They had also focused on the security situation.
Mr Paisley Jr said while there was pressure for concessions on the scaling down on security, the recent election result in November emphasised the need for those concessions to stop.
He added: "I think it is fair to say that the election on November 26 stopped the concessions to the Provisional IRA.
"From our point of view, it is important that that full stop to the concessions is maintained and the Government does not make it a pause or a comma and then proceed with concessions later on.
"The only way forward now is for political progress to be made and the Government to listen to the voice of the people."