Lawson qualified 18th at the season-opening Australian Grand Prix and crashed out of the race. In China last weekend, he qualified last for both the sprint and the grand prix, and finished 14th and 12th.
World champion Verstappen was second in Melbourne and fourth in Shanghai. The next race is the Japanese Grand Prix, from 4-6 April.
Lawson, 23, admitted he found his demotion “tough” but said he is excited to work with his former team Racing Bulls.
“Being a Red Bull Racing driver has been my dream since I was a kid, it’s what I’ve worked towards my whole life,” he wrote on Instagram.
“I’m grateful for everything that’s brought me to this point. To every one of you who’s stood by me, thank you for all the support. It means the world.”
Marko said that Tsunoda, 24, would be given “to the end of the season” at Red Bull to prove himself “because we believe he can do the job”.
Asked why the Japanese was the right driver now, when they had decided at the end of last season that Lawson was a better bet, Marko said: “Tsunoda made a big step. It’s strange after four years, now in his fifth year, he is a much stronger personality, he has more confidence and he did two very good races, it’s just his strategy didn’t work at Racing Bulls.
“In this case, a very difficult car experience is something that will help. That was our thoughts.”
Marko said that Red Bull decided not to give Lawson another chance at the Japanese Grand Prix, which is the first race this season to be held on a circuit Lawson has experienced before, because “we were worried that his self-confidence is so damaged that he couldn’t bring his normal performance”.
He added: “And on the other hand we have two drivers for the constructors’ championship but also to support Max strategy wise, if you have two drivers top five or eight it is easier to max a strategy that favours the number one driver.”
Marko insisted that the swap with Tsunoda was “not a demotion” for Lawson.
“He’s not kicked out of F1,” Marko said, “and Racing Bulls will give him the chance to recover and his career will start again.”
Marko pointed to the experience of drivers Red Bull had previously dropped as evidence that Lawson could rebuild his career.
Marko said: “For the benefit for him, he goes back to Racing Bulls, which has a car capable to be top 10 in qualifying and the race.
“Just look in the past, it was (Pierre) Gasly, it happened the same, also to (Alex) Albon and they recovered and they are now competitive F1 drivers.
“On top of it, the RB21 is a car which is not the fastest car but nevertheless very difficult to drive and Max can handle but not at this stage Liam.”
