[intransitive, transitive] to try to end a situation between two or more people or groups who disagree by talking to them and trying to find things that everyone can agree on (Oxford)
[transitive] mediate something to succeed in finding a solution to a problem between people or groups who disagree (Oxford)
to talk to two separate people or groups involved in a disagreement to try to help them to agree or find a solution to their problems (Cambridge)
The Secretary-General was asked to mediate in the dispute. (Oxford)
The UN attempted to mediate a solution to the conflict. (Oxford)
Negotiators were called in to mediate between the two sides. (Cambridge)
mediate in the dispute
attempted to mediate a solution
called in to mediate
Intervene
Referee
Argue
Refuse
Mediation
Mediator