Marathon all-night negotiations in Belfast to resolve outstanding peace process issues in Northern Ireland have broken up without reaching an agreement.

Northern Ireland Secretary Theresa Villiers said it was disappointing, but the failure to reach a comprehensive agreement should not be seen as the end of the road in seeking to find a way forward on difficult and divisive issues.

Talks broke up in the early hours of Tuesday morning after discussions that had reached a climax under the chairmanship of the former US diplomat Dr Richard Haass.

The talks covered a range of issues from Northern Ireland's history including unsolved murders from the Troubles, the route of loyalist parades and the flying of national flags – all matters that have repeatedly brought violence back to the surface of life in Northern Ireland despite the Good Friday Agreement that allowed the devolution of power to the assembly at Stormont.

Haass had presented the parties with the seventh draft of a document intended to resolve outstanding controversies of the Irish peace process. Among the proposals was the establishment of a new "Implementation Reconciliation Group" that would take six months to discuss an action plan on three major issues still dogging the power sharing settlement between the two communities in Northern Ireland.

Haass had described the agreement as a "remarkable opportunity to make bold choices to address the issues that hold us back". Sources at the talks had held out hope of an agreement by the early hours of Tuesday.

After Haass announced that the negotiations had broken up, Villiers said: "I would encourage [the five parties] to maintain the momentum that their efforts, working with the Haass team, has created. For our part, the UK Government will look at how we can best facilitate this."

Northern Ireland's justice minister accused the two main unionist parties of putting their electoral fortunes above any deal that could have resolved key post-peace process issues like controversial parades and flags.

David Ford claimed the unionists had failed "to face down the extremes over flags – but parties who ducked it clearly rely on those extremes to sustain their vote. It is time that parties stopped hiding behind process and committed to product.”

The Alliance leader and justice minister singled out the unionist parties' failure to support a legally binding code of conduct on loyalist marches as one of the main reasons for failure in the early hours of Tuesday morning.

The Democratic Unionists, Ulster Unionist party, Sinn Féin, the SDLP and Alliance had been locked in negotiations up until 5am at the Stormont Hotel in east Belfast.

The prime minister, David Cameron, said the failure to achieve a breakthrough was disappointing, but urged the parties to “keep going”.

“Although it is disappointing the parties have not been able to reach full agreement at this stage, these talks have achieved much common ground, providing a basis for continuing discussions,” he said.

“There is a shared commitment to making progress on these very difficult issues that continue to be a focus for tension and division across the community.

“I urge the parties to keep going. I also want to thank Dr Richard Haass and his team for their dedicated work.

“The government and the Northern Ireland parties will continue to work together to strengthen further the foundations for peace, stability and prosperity in Northern Ireland.”

Theresa Villiers, the Northern Ireland secretary, said it was “disappointing” but the break down of the talks was not the end of the road.

“The reality is if you look at issues of identity, some people would argue that it’s been a problem for the last 800 years. In many ways, it’s not surprising that it can’t be fixed in three months,” she told the BBC Radio 4 Today programme. “If there were easy solutions, then it would have been part of the Belfast Agreement agreed in 1998.”

Asked whether the UK government should be more involved, she said she has been active behind the scenes but it was important for Northern Ireland politicians to take the lead.

Villiers said there were also wider problems around segregation in Northern Ireland that need to be discussed.

“I’d urge the work to continue on these divisive issues, the importance of this broader project to see an end to sectarian division,” she said. “Flags, parades and the past are an important part of that, but we also need to see progress on more kids sharing their education, more neighbourhoods being less segregated than they are at the moment. It’s also important for the Northern Ireland executive to be working with the government on our shared objective of boosting the economy.”

In a hard-hitting assessment of the unionists' attitude to the parades and flag issues, Ford said: “On parades new structures have been proposed. But the real issue with parades was never about structures – the problem was behaviour. The desperate attempts by the unionist parties to resist an effective code of conduct for marchers and protesters showed that very clearly. So while we have a new approach to structures, it remains to be seen whether there will be any change in behaviour.

“If the attitude to flags is anything to go by, we don’t hold out much hope, because the biggest disappointment of this process has been the refusal to face up to the issue of flags."

Talks chairman Haass and his co-chair Meagan O'Sullivan were unable to persuade the parties to accept the seventh draft of a 38-page agreement on flags, marches and the past.

Commenting on the breakup of the talks, Haass said all five parties had "given it their best" and were "prepared to continue" with the process.

"It would have been nice to have come out here tonight and say we have got all five parties completely signed on to the text," he said.

The Sinn Féin president, Gerry Adams, said his negotiating team believed there was a "basis for a deal in the proposals put forward".

He said the team would recommend it to the party's executive, though he said the proposed deal was "not perfect".

"I'm sure there will be a lot of disappointment out there as people come to terms with the fact that there doesn't appear at this point to be an agreement," he said.

There appeared to be more agreement about issues to deal with past Troubles crimes and their legacy among the parties with the establishment of a new investigative body.

One of the most controversial issues is the legacy of the past conflict in which 3,500 people died. Around 3,000 of those killings remain unsolved and the Haass talks discussed the creation of a new police-investigative body to re-examine these cases. Thousands more suffered injuries and psychological trauma in three and a half decades of violence.