An indication is making a move. In OTB chess, one can say that he doesn't agree too. In both cases, after you offer a draw make your move (and hit the clock in OTB), so that you won't lose time. You are not supposed to wait for a reply in your own time, neither is your opponent obliged to tell you his decision any time soon - a draw offer can be accepted at any time before making the next move, when the offer stops being valid.
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When you offer a draw is there any indication they have refused or does the your turn just stay on ?