On Thursday, Perez stressed that he now feels he has an equal opportunity to succeed at Red Bull and is supported by the team.
However, the Saudi Arabian GP winner added that before he arrived at Red Bull in 2021 "they were just going racing with two cars because they had to".
The clear implication was that his immediate predecessors, Pierre Gasly and Alex Albon, did not enjoy the same level of support that he now enjoys as Verstappen's team-mate.
However, Horner insisted that the team has never favoured one driver over the other.
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"Well, that's the first I've heard him saying that," said Horner when asked by Autosport about Perez's comments.
"We always have run two cars since we entered the sport in 2005. And we always want to have the best two drivers that we can in the car, and I think it's great to see Checo doing certainly a great job now.
"In 2021 he came into the car off the back of the COVID season and at the end of a set of regulations, and he struggled with that car. Last year, he was definitely more at home within the car and two of our 17 victories he achieved.
"He's got out the blocks well again this year. But we're only two races into the season and it's an awful long, long way to go.
"And as a team, we've always strived to give both drivers the best opportunity and the best equipment we can and then it's down to what they do on track.
"And that's whether it's Max and Checo, or Daniel [Ricciardo] and Max, or Daniel and Seb [Vettel], or Mark [Webber] and Seb, or we could even go back to David Coulthard and Mark Webber.
"So that's the way we've always rolled and it's down to what they do on the circuit at the end of the day that counts."
Horner praised Perez for his strong start to the 2023 season as he picked up the pieces to win in Jeddah after Verstappen's driveshaft problem in Q2 left him to start in the midpack.
"He drove some great races last year," he said.
"You only have to think back to Singapore, for example, which was an outstanding victory for Checo last season.
"But he's done a great job in the first two races this year, his confidence is sky high, and that's exactly what we want. We want two drivers that are going to be pushing and challenging each other."
Horner downplayed any suggestion that tension could build between Verstappen and Perez if they become championship rivals.
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"There's no reason why it should," he said.
"I mean, they're both competitive animals, and they're both racing drivers at the end of the day, but they know the rules of engagement, in terms of it being team first.
"And particularly at this stage of the year, where we know that we don't have the development capability that other teams have in terms of wind tunnel time as the season goes on.
"So for us it's hugely important to bag as many points as we can, get as many into the championships as we can, early on, because we know the others are going to come back at us in the second half of the year."
