This is the problem in any negotiation, whether it be between groups or between individuals. People's positions are so entrenched, and they tend to dig in their heels if anyone talks about even sitting at the same table.
The first step is to find common ground, no matter how far apart people seem to be. This can be accomplished by a skilled negotiator, who usually needs to move back and forth between the parties involved at first. It is always possible to find some common ground, even a very small goal that both sides agree it makes sense to pursue. For example, between pro-choice and pro-life groups, there is no disagreement that unwanted pregnancies are best prevented. That is a common goal that both sides can work towards.
The second step is to try to get both groups to work together on the common goal. This means that people will be spending some time together working on something they agree on, a sure way of building some empathy and respect for the position of another.
Next would be a second attempt to get people back to the table, either to try to find another common goal, or even to try to resolve thornier issues.
This is likely to be a recursive process, moving back and forth between the steps, in the hope of achieving common ground on the central disagreements. Peace is a process, not a date in time. It cannot occur without some common mission or empathy, and the peace-making process must include both for it to come to fruition.