How to compare responses from two runs for regression testing

How to compare responses from two runs for regression testing?

I have a collection which runs a sequence of requests to an API. Assuming all responses were correct I want to save all of the responses somewhere automatically and in the next run I want only to check if the responses are the same.

Purpose is that we assume that the current responses are tested and are ok, and we only want automatically test if any of our code changes introduced new bugs in the already released API.