Friend is being distant after a fight?

My guy friend and myself had a massive fight. We were not talking for a week, until I reached out to him. He told me what hurt him and told me what I should do to avoid upsetting him and I promised him I'd work on it.

He asked for space, which I said I'd respect and leave him be. He ended up messaging me the next day and since then have been messaging daily, but he has been very cold despite messaging every day.

I thought it would be best to give him more space to make himself feel better, however he would get even more upset and think I genuinely do not want to be friends with him. So I am replying to him to be polite, but of course I want to talk to him, however he is making it difficult.

I do try to keep the conversation light-hearted most of the time, playful and sometimes also serious discussions about the world. But he still is cold. I know I hurt him, and I thought he would need a lot of space, but he keeps texting me daily with coldness?

I am not really sure what to do. I am trying to mend the relationship back to how it was similarly but he is being very cold about it.

Should I give him more space or just follow his lead in coldness?

Friend is being distant after a fight?
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