Turn down an invitation:

Sorry, I am really busy now.

I'm going to be busy then.

I would love to, but I am too busy today.

I have an appointment then/at that time.

I've got another commitment at that time.

Could we move this to another date?

Could we do this at another time?

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If someone calls on a phone and you don't have time:

I'm tied up.

I'm in a rush/ in a hurry/busy now/ in the middle of something/running short of time.

I have no time now.

I really don't have time to talk now, can we talk later？