"All people have to do is look at the pain and suffering that violence is producing elsewhere in the world today. I hope we can make good progress," Mowlam, the minister in charge of the British province, told reporters.
She spoke as talks reopened in the provincial capital aimed at ending a deadlock over guerrilla disarmament that has held up progress on a peace deal signed a year ago.
Earlier this month, the British and Irish prime ministers, Tony Blair and Bertie Ahern, published a compromise plan for forming the new Belfast government, the intended centerpiece of last year's peace accord.
But the Irish Republican Army and its allied Sinn Fein party rejected it.
The premiers' proposal called for Sinn Fein to receive its two allotted posts in the envisioned 12-member government if, in exchange, the IRA promised to start disarming within a month.
"That was the two prime ministers' best guess as to how we might move forward," Mowlam said. "But let us not be under any illusion. Any alternative must be acceptable to both traditions. Otherwise, this is not going to work. If people are only prepared to fight their own corner, then progress cannot be made ... and nothing that the prime ministers can do will help."
Protestant leader David Trimble insisted the IRA must hand in some arms before its Sinn Fein political wing takes up its two seats on a coalition cabinet at the province's helm.
Blair and Ahern are ready to fly in if the politicians find a compromise, but they aren't expected to arrive before Thursday and will come only if progress is made. "Even prime ministers are subject to the law of diminishing returns," one senior source close to the talks said.
Sinn Fein leader Gerry Adams and his chief lieutenant, Martin McGuinness, met Trimble and Reg Empey, another senior member of Trimble's Ulster Unionist Party, before joining other politicians for round-table talks.
"All talks are progress," said McGuinness, who is Sinn Fein's contact man on an international disarmament commission.
His party, which shares the IRA's goal of a united Ireland, had not moved from its stance that the declaration rewrote the original peace deal's vision for disarmament.
The accord foresaw disarmament being completed by May 2000. It set no start date for a process that the two governments, centrist parties and many in the province want to start sooner.
The powerful Ulster Unionists view the Blair-Ahern proposal as "a basis for negotiation" but want it clarified. They are sticking to their position that a "credible and verifiable beginning" to disarmament must take place before Sinn Fein enters the cabinet.
The peace deal brought hope after 30 years of bombs and bullets which claimed more than 3,600 lives.