President Donald Trump's re-election team has rejected claims that a social media campaign by Tik-Tok users and K-Pop fans was behind the lower-than-expected turnout for Saturday night's Oklahoma rally.
Teenagers are said to have booked tickets without intending to turn up so as to produce empty seats.
The Trump 2020 team said one million requests had been made for tickets.
But it insisted that it had weeded out bogus reservations.
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."
Former Republican strategist and a critic of Mr Trump, Steve Schmidt, said teenagers across the US had ordered tickets without intending to turn up. His 16-year-old daughter and her friends had requested "hundreds" of tickets.
A number of parents responded to Mr Schmidt's post saying that their children had done likewise.
House representative, Alexandria Ocasio-Cortez, a leading progressive figure, praised the young people and K-pop fans she said had "flooded the Trump campaign w/ fake ticket reservations".
It is unclear how many of the hundreds of thousands of ticket reservations touted by the Trump campaign were fake, but one TikTok video from 12 June encouraging people to sign up for free tickets to ensure there would be empty seats at the arena has received more than 700,000 likes.
The video was posted after the original rally date was announced for 19 June.
The news had sparked angry reaction because it fell on Juneteenth, the celebration of the end of US slavery. The location of the event, Tulsa, was also controversial, as it was the site of one of the worst racial massacres in US history.
After news of the smaller crowd numbers emerged, the account's owner Mary Jo Laupp praised the response, telling young people who were too young to vote: "Remember that you, in doing one thing and sharing information, had an impact."
If true, it would not be the first time social media users have shown their political impact in recent weeks.
Fans of K-pop, South Korea's popular music industry, have been active in drowning out hashtags used by opponents of Black Lives Matter (BLM) in recent weeks, and raised money following the death of African-American George Floyd last month.
The BBC's Anthony Zurcher, who was in Tulsa, says rally organisers always approve more tickets than there is space, so pranksters filling out reservations would not have stopped legitimate supporters from attending.
However, it appears they convinced the Trump campaign that more people were interested in going than actually were.
The campaign had boasted of about one million RSVPs but if even half of those reservations had been legitimate the rally would have seen a far greater attendance, he adds.
There had been health concerns about holding the rally, the first of its kind since lockdown measures began in many US states.
Those attending the rally had to sign a waiver protecting the Trump campaign from responsibility for any illness. Hours before the event began, officials said six staff members involved in organising the rally had tested positive.
The pandemic was one issue Mr Trump touched on in his wide-ranging, almost two-hour-long speech to cheering supporters in Oklahoma, a Republican heartland.
There had been fierce opposition, including a legal challenge rejected by Oklahoma's Supreme Court, against holding the rally during the pandemic on health grounds.
Some feared the rally could become a coronavirus "super spreader" event.
More than 2.2 million cases of Covid-19 and 119,000 associated deaths have been reported in the US, according to data from Johns Hopkins University.
What did Trump say?
In his opening remarks, Mr Trump said there had been "very bad people outside, they were doing bad things", but did not elaborate. Black Lives Matter activists were among the counter-protesters to gather outside the venue before the event.
On the coronavirus response, Mr Trump said he had encouraged officials to slow down testing because it led to more cases being discovered. He described testing as a "double-edged sword".
"Here is the bad part: When you do testing to that extent, you are going to find more people, you will find more cases," he told the cheering crowd. "So I said 'slow the testing down'. They test and they test."
The coronavirus, Mr Trump said, had many names, including "Kung Flu", a xenophobic term that appears to be a reference to China, where Covid-19 originated.
Almost 120,000 people have died with Covid-19 in the US since the pandemic began, a number that health experts say could have been much higher had testing not been ramped up. Testing, health officials say, is important to understand where and how widely coronavirus is spreading, and therefore prevent further deaths.
A White House official later said the president was "obviously kidding" about Covid-19 testing.
Taking aim at his Democratic presidential rival, Mr Trump described Joe Biden as "a helpless puppet of the radical left".
The president also struck a combative tone when he touched on anti-racism protests - and the toppling of statues - which began after the killing of an unarmed black man, George Floyd, by police in Minneapolis.
"The unhinged left-wing mob is trying to vandalise our history, desecrate our monuments - our beautiful monuments - tear down our statues and punish, cancel and persecute anyone who does not conform to their demands for absolute and total control. We're not conforming," he told the crowd.