The Red Bull junior contested five races for the team at the end of the previous season, ending his campaign with a best finish of fourth in Bahrain.
"Max, if you look at his performance in the second half of the (last) year, was the second-highest points scorer to Lewis", Horner said.
That was the assertion of his Red Bull boss Christian Horner, who told reporters on Tuesday the team could "provide him the tools to do the job". "I think he's probably the driver that they fear the most".
Verstappen was the sport's youngest driver when he debuted with Red Bull-owned Toro Rosso as a 17-year-old and the youngest victor at 18 at the 2016 Spanish Grand Prix.
Former champions Red Bull, who finished third overall behind champions Mercedes and Ferrari a year ago, have switched from Renault power units to Honda for the season starting in Australia on March 17. "We've seen in the past year that depending on the circuit, those penalties can have minimal consequences". "He's just much more rounded through experience", added Horner. "He's just in a better place to be able to deal with the pressures that are placed on him".
Asked about Verstappen's public service punishment for his actions in Brazil, which saw him forced to attend a Formula E race in order to observe the work of the stewards, Horner admitted that it was an enlightening experience for the youngster.
Mercedes and Red Bull are launching their new 2019 cars on the same day next week, February 13, as the sport's teams give a first glimpse of how they have interpreted the new aerodynamic rules for this year.
"He came back and went, 'Crikey, these guys have got hard decisions to make".
Horner was sure the Honda partnership would be very different.
"Red Bull Technology have been working with Honda for 12 months now, having supplied the gearbox and drivetrain solution for Toro Rosso". It is exciting, although that will really come when I sit in the auto.
"[My goal is] try to win as many races as possible".
"This is the first time that Red Bull and Honda have collaborated, and we know that at the beginning of a relationship, it always takes a little time for things to become automatic and you get the most out of it".