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.
The team's campaign director said in a statement that "phony ticket requests never factor into our thinking" as entry to rallies is on a first-come first-served basis. Brad Parscale blamed the media and protesters for dissuading families from attending.
"Leftists and online trolls doing a victory lap, thinking they somehow impacted rally attendance, don't know what they're talking about or how our rallies work," Mr Parscale said.
"Registering for a rally means you've RSVPed [confirmed attendance] with a cellphone number and we constantly weed out bogus numbers, as we did with tens of thousands at the Tulsa rally, in calculating our possible attendee pool."