Red Bull is already in talks to extend its engine deal with Honda beyond 2021.
Both Red Bull-owned teams announced on Wednesday that their Honda contracts have been extended for one more year. The existing deal had been set to run out in 2020.
"This is a great relief for us," Dr Helmut Marko told the Austrian broadcaster Servus TV.
"We are very satisfied with Honda."
It seems that Honda's biggest concern about the new era of Formula 1 from 2021 is the costs.
Liberty Media and the FIA are working hard to cap costs for the teams, but the engine regulations are staying the same and do not fall under the budget cap.
"Obviously, good results will help to continue the (F1) programme, but the balance between the input and the results also has to be right," Honda's Masahi Yamamoto told Auto Bild.
"It is not easy to get to the top and we have to manage to do so in a financially sound way."
Marko says talks about extending the deal beyond 2021 are already underway.
"We are already talking to Honda about a further cooperation for 2022 and 2023," he revealed.
"That depends to a large extent on the cost savings, but the FIA is now starting to recognise that.
"They have expressed the intention to freeze the engines from 2021. That would ensure that the development would almost stagnate and the costs can also be drastically reduced."
Marko said the way the conversation about engine costs develops will be key to Honda's future in F1 beyond 2021.
"It can indeed prove to be crucial for Honda and would allow for further cooperation," he said.
