A meeting which was supposed to have been attended by Ian Paisley and Gerry Adams has been postponed at Stormont.
The meeting between the party leaders was postponed
Mr Paisley and SF's Martin McGuinness are due to become shadow first and deputy first ministers on 24 November.
But the DUP is insisting that a pledge of support for policing and for law and order is in place before then.
Speaking after the postponement, Mr Paisley said the DUP's assembly members had "passed a unanimous vote in the leadership of this party".
"We have a document issued by the two governments. It is not our document. It is their document," he said.
"We are going to take time to consider it and give to the people of Northern Ireland our findings on the matter and also we are going to have a full consultation with the people."
Speaking on Tuesday, Northern Ireland Secretary Peter Hain said a separate committee would "urgently discuss" the "differences in the understanding" of what the pledge meant.
Mr Hain described the postponement of the meeting as "a glitch".
"I think we will get through this, and we need to get through this - for otherwise I close the place down - the parties all understand that," he said.
Last week's St Andrews Agreement stated that before the government legislated on the pledge of office, "it will consider the outcome of further Preparation for Government Committee discussions on policing and the rule of law".
Mr Paisley and Mr Adams had been expected to attend a meeting of the new Programme for Government committee until the DUP raised objections on the pledge issue.
The postponed meeting was supposed to discuss priorities for the executive, which is scheduled to take power next March.
It was seen as significant that Mr Paisley and Mr Adams were to sit at the same round table for talks at Stormont.
BBC Northern Ireland political editor Mark Devenport said: "The DUP want Martin McGuinness to swear to support law and order and the PSNI when he is nominated as deputy first minister on November 24th.
"But republicans are resisting that, not least because that will be before they hold a special party conference to decide their policing policy."
Speaking after the postponement announcement, SDLP leader Mark Durkan said people needed "to avoid head-staggers at this stage".
"Undue problems are being created, or generated, in and around the questions about pledge of office and what will happen on the 24 November," he said.
Ulster Unionist leader Sir Reg Empey said it was a "very fluid situation" and what he described as "panic politics".
"This indicates complete chaos as to the management of this process," he said
Alliance Party leader David Ford said all parties should be around the table so we can actually address the outstanding issues as a package".
Meanwhile, DUP MEP Jim Allister expressed concern that the IRA is not obliged to disband its army council under the St Andrews Agreement.
Mr Allister stressed he was not rejecting the package, but wanted to see healthy debate within the party.
The Northern Ireland parties have been given until 10 November to respond to what the governments are calling the St Andrews Agreement.
It was published after intensive three-day talks between the parties at St Andrews in Scotland.
If all goes to plan, a first and deputy first minister will be nominated on 24 November and the devolved institutions will be up and running by 26 March.