OTTAWA, Ont. - Three of four federal parties have reached an agreement that will give MPs access to thousands of sensitive Afghan detainee documents, starting this summer.

But New Democrats refused Tuesday to sign on, insisting the process is a sham and renewing calls for a public inquiry as the only way to ferret out the truth.

And they called on Commons Speaker Peter Milliken to find that the agreement falls short of his historic April 27 ruling, in which he confirmed MPs' absolute right to unfettered access to all uncensored detainee documents.

Milliken said he'll rule "shortly" on the NDP's request, presumably before the House of Commons breaks as early as Thursday for the summer.

"The whole process, as far as we're concerned, does not get at the truth and will not get at the truth and we will not sign on to it," NDP defence critic Jack Harris said after a final negotiating session among all parties early Tuesday.

Harris, the NDP's lead negotiator, said the agreement reached by the governing Tories, Liberals and Bloc Quebecois won't give MPs the access they need.

He said documents the government claims to be matters of cabinet confidentiality or solicitor-client privilege will be kept from MPs. A panel of jurists will vet the material and decide whether MPs can see it.

That leaves MPs out of the loop and is unacceptable, Harris said.

In the Commons, NDP Leader Jack Layton suggested the current and former governing parties have conspired to ensure MPs will never know "the role that was played by both Liberals and Conservatives in covering up what they knew about torture in Afghanistan." He said Prime Minister Stephen Harper should be "ashamed."

Harper congratulated the other opposition parties for reaching an agreement but castigated the NDP for taking "an extreme and irresponsible position on this matter."

Tory House leader Jay Hill said it's "unfortunate" the NDP could not join the agreement, but told Milliken the deal represents the views of the "vast majority" of MPs.

"In the end, the agreement that was reached reflects the fact that everyone there had to put some water in the wine," Hill said.

"It was certainly our hope all along, as the government and the people we had at the table, that we could arrive at an agreement that would encompass all members of Parliament and all political parties. Unfortunately, that has not proven to be the case."

He said the NDP organized a news scrum even before the meeting adjourned.

"It really calls into question whether they, in fact, were negotiating in good faith this morning."

From the outset of talks, Liberal House Leader Ralph Goodale said the NDP seemed to want negotiations to fail, even objecting to requiring security clearances for MPs who'll be allowed to review the documents.

He dismissed as "horsefeathers" the NDP's claim that Liberals caved on the deal to avoid triggering an election.

Liberals contended last-minute changes to the deal -- settled after the NDP walked out of Tuesday's talks -- removed or ameliorated most of the fourth party's concerns.

The issue is now in Milliken's hands.

He ruled April 27 that Parliament has a right to see the Afghanistan documents, but urged the parties to broker a deal that would allow access while preserving national security.

"Where we go from here, that's up to the Speaker," Harris said, acknowledging the possibility the NDP could be left out of the process entirely.

However, should Milliken agree with the NDP, Harris then plans to introduce a motion laying out a process that he says would give more access to the sensitive documents.

The papers relate to allegations that prisoners were routinely tortured after they were turned over to Afghan authorities by Canadian soldiers.

Goodale said the agreement is a good one that addresses all the issues and gives MPs access to most documents as long as the government acts in good faith.

The government has surrendered its "unilateral authority to say what's relevant and what's necessary," he said. Instead, an ad hoc committee of MPs and a panel of three experts, approved by the opposition parties, will make those decisions.

"Parliament has taken charge of the process," Goodale said, noting the experts will be impartial.

"What's critical is the panel of experts is not a government entity; it's not an arm of the government. It is to be selected by all of the parties participating in this process together. In other words, all of the parties have a veto over who's going to be on the panel of arbiters."

Bloc House leader Pierre Paquette said the ad hoc committee of MPs should be able to begin poring over as many as 40,000 documents by the end of July.

Under the deal, one MP and one alternate from each of the three parties that have signed onto the agreement will swear an oath of secrecy. They will be entitled to see the censored and uncensored versions of most documents and determine whether they are relevant to holding the government to account.

Former leader Stephane Dion will represent the Liberals on the ad hoc committee, with MP Bryon Wilfert as the alternate. The Tories and Bloc have not yet named their representatives.

Documents deemed relevant will be passed on to the panel of three eminent jurists -- who have yet to be chosen and must be approved by all three parties. The panel will determine how -- or if -- the documents can be publicly disclosed without jeopardizing national security, international relations or the safety of Canadian troops in Afghanistan.

The panel could choose to summarize or censor some documents.

Any documents deemed by the government to be cabinet confidences or legal advice will be directly referred to the panel, which will determine whether they can be seen by the ad hoc committee.

New Democrats predicted the government will take this route on virtually everything, tying up the process endlessly.

But Goodale said Liberals won't tolerate any attempt to obstruct the work of the ad hoc committee.

"If we find that the government is not behaving in good faith, then we will report that to the public and we will blow the process up," he said.

Should it prove necessary, he said Liberals would go back to the Speaker for a ruling that the government was subverting the will of Parliament.