Met with is different from met if we mean 'have a meeting with' rather than just 'bump into'. Having a meeting usually lasts a while, so its nature is more imperfective. I can imagine John or the speaker working at the supermarket, and in that case, I have met with John at the supermarket today should be pretty idiomatic."I have met with John ..." is what I would say is the more usual form of the past perfect sense, and that would be used when the following sentence described a purpose for the encounter.
I have read the explanation of Wilma's and I am not sure if it always works.I met John in the supermarket today would be my choice. Normally, including a time reference like today could generate
past perfectpresent perfect!!!
It sounds as if an unintended action requires PAST SIMPLE while an intended (scheduled) requires PRESENT PERFECT)I usually try to simplify things. This time I will complicate them.
1. I met John in the supermarket today. I bumped into him, encountered him.
2. I had an appointment to meet with a person for the first time. I did so. I am now telling a colleague about the meeting and its outcome:
I have met John in the supermarket today. [As scheduled.] We have agreed to a plan for next week's bank robbery. He seems like a charming burglar.
You could use the past tense in the sentences above, but for a narrative description the present perfect works well.