Published Wednesday, 03 February 2010
After eight days of negotiations, Woodward told MPs at Wednesday's Northern Ireland Questions that with "good political will" there could still be a "reasonable" agreement.
But he warned that failure to achieve agreement would put much of the achievements of the peace process at risk.
Read Ken Reid's blog: Party time
No further talks have been scheduled between the DUP and Sinn Fein on Wednesday, amid mounting speculation that the outcome of the negotiations will depend on the next meeting of the DUP's assembly team.
On Tuesday, the DUP denied there was any split within the party ranks despite reports that 14 MLAs opposed the policing and justice deal put forward by Peter Robinson the day before.
"An essential agreement of the current discussions must be a consensus that can command community confidence", DUP's South Antrim MP William McCrea told the House of Commons.
"Without that community confidence, no matter what pressure is placed on me or my colleagues, the DUP will not be buying into any deal."
He said progress had been made but "more progress had to be done".
Mr Woodward replied: "Everyone must have confidence but of course confidence doesn't belong to any one community. One of the principles here is that it must indeed command support from everyone in Northern Ireland.
"The Assembly has been up and running for nearly three years. This business remains to be done, we believe the confidence is there, it is now time to summon leadership and courage and act."
Answering a question from the Tory chairman of the Northern Ireland Select Committee, Patrick Cormack, Mr Woodward warned:
"Patience is required, but equally we must be careful not to try people's patience to distraction.
"Unfair failure to make progress would not be rewarded, and I don't mean by any particular process now, but by the people of Northern Ireland.
"We have changed their lives by the peace process, we have secured it in the political process.
"It is right to make progress but we do indeed now sit on the edge."