Teenagers are said to have booked tickets without intending to turn up so as to produce empty seats.
But the Trump 2020 team said it had weeded out bogus reservations.
Mr Trump had said he expected one million to come.
The Bank of Oklahoma Center venue in Tulsa seats 19,000. The event was also planned to extend outside, though that part of it was cancelled.
The Tulsa fire brigade is quoted as saying more than 6,000 attended, but the 2020 campaign suggested the figure was much higher.
