Dear Sameer,
Involvement in a physical fight is a serious matter. It needs to be investigated by conducting a domestic inquiry and punishing the guilty with severe consequences. A warning letter is a mild form of punishment.
Apart from handling the case from a legal perspective, you also need to consider the organizational climate. Why did the situation escalate to this point? Why are employees feeling so frustrated? Do they have adequate resources to perform their duties? Have you clearly defined areas of responsibility? Do you have a grievance handling policy, and if so, how do you assess its effectiveness? What role does the manager play? Is the manager overly accommodating towards superiors but behaves differently with subordinates?
You may see this incident as an isolated occurrence, but there seem to be deeper underlying issues that require attention from you and your management.
Thanks,
Dinesh V Divekar