US diplomat Richard Haass has admitted that equal progress may not be possible in all three of the key areas he has been brought in to address.
He has also admitted that his timetable for solving issues such as parading, flags and the past by Christmas may have been "ambitious".
Dr Haass jetted in from New York yesterday before hosting the opening round of critical talks aimed at resolving some of Northern Ireland's most divisive issues.
He is meeting representatives from each of the five parties in the Stormont executive before holding plenary talks later in the week.
Yesterday he met with Sinn Fein and the SDLP, while the DUP, Ulster Unionists and Alliance are on today's agenda.
The ex-White House special envoy is attempting to achieve agreement on three issues – flags and emblems, parades and dealing with the legacy of the past.
Speaking to the media before talks got under way, and flanked by Harvard professor and experienced negotiator Dr Meghan O'Sullivan, who is a senior member of his team, he warned peace process gains could not be taken for granted, with work still needed to tackle the unresolved issues.
Asked if he was more hopeful of success on a particular topic, Dr Haass admitted there may not be equal progress on every issue.
"I would hope to make progress on all three areas – that's our goal," he said. But he added: "It may be at the end of the day that the potential for equal progress is not there."
At the weekend, Dr Haass indicated the talks could also include issues such as segregated education and housing. However, he appeared to backtrack somewhat on that yesterday.
"The focus will be on the three issues," he added. "I didn't mean to suggest that now there was a fourth agenda so, if that was the conclusion that some took, that wasn't meant to be the case."
While Dr Haass said it was conceivable that other issues would arise during talks and that good progress could create momentum, the timetable was already ambitious.
"We have three and a half months, it is already pretty ambitious the focus on these three areas," he added.
Dr Haass said the disorder surrounding parades over the summer showed the urgency of agreeing a way forward.
"There's been tremendous progress but there is still a real need to move things forward and that is why we are here," he said.
"I think this last summer was something of an indication or something of a warning that one should not take the improvements for granted."
Stressing the importance of compromise, Dr Haass said no outsider can substitute for the willingness of insiders to reach agreement.
He added: "We look forward to all sorts of give and take in these days and obviously subsequent visits. The goal here is to come up with a consensus document that ideally would be both broad and deep, dealing with these three sets of issues, and that is our goal at this point."
After meeting Dr Haass in an encounter lasting just over an hour, Deputy First Minister Martin McGuinness emerged with the rest of the Sinn Fein delegation and expressed optimism that resolution could be obtained.
"We are approaching all of this in problem-solving mode," he said.
"These are very, very serious issues that badly need resolution and we are very determined to play a positive and constructive role during the course of these discussions to find a resolution to these problems, because quite honestly that's what people want."
SDLP negotiator Alex Attwood said his party had told Dr Haass that whether there was agreement or not, he should publish his findings.
Party leader Alasdair McDonnell said the SDLP was "totally and unconditionally committed to seeing this process through".
"We have ambition. We believe absolutely that these talks can be comprehensive and bring closure to the issues that were parked 15 years ago."
Earlier, Dr McDonnell said that Dr Haass said spend most of his time outside the talks room, exerting pressure on those inside.
"If there's a will and if there is a determination and if there is a generosity, yes, these issues are resolvable. I think we are all agreed that dealing with the issue of the past might be the most difficult of all, but I think if people come at this with a good heart, huge progress can be made."
Deputy First Minister Martin McGuinness (right)