Sinn Féin said it was “deeply disappointed” with the outcome of the talks and blamed DUP demands for a concession on loyal order parades for blocking an agreement.
Deputy First Minister Mr McGuinness, flanked by party colleagues including president Gerry Adams, said: “I believe we have displayed extraordinary patience and commitment over the past 18 months as we sought to persuade the Democratic Unionist Party to be partners of progress.
“Over recent days the two Governments have joined that effort.
“The decision by the DUP, at the behest of the Orange Order, to make the abolition of the Parades Commission a pre-condition for the transfer of powers on policing and justice flies in the face of all that.”
Mr McGuinness claimed the demand had made agreement difficult, adding: “Many are speculating that this was the real intention.”
He said that, despite progress on policing, no final deal had been agreed.
“I am very deeply disappointed about that,” he said.
The senior Republican had made his feelings known in a private meeting with party leaders and in subsequent meetings with the premiers.
The party would nevertheless study the proposals tabled by the two Governments, he said.
“But one thing is certain — and it is absolutely certain as far as we are concerned — that citizens’ rights and entitlements will not be made subject to a unionist veto or an Orange Order pre-condition.”