"I don't know if you can say we are on a mission. That is the easy term to use. But I think we are aware that the only way to let up is by winning," Mbappe told French broadcaster M6 after an eventful quarter-final tie in which he had a first-half penalty saved but later opened the scoring.
"We are in the semi-finals and we are very pleased. There is still a long way to go and we are aware that what awaits is going to be even harder, but we are ready," he added.
"We are ready to confront everything we come up against, so we will recuperate in peace and watch tomorrow's game to find out who we will face next."
Mbappe had a hand in Ousmane Dembele's goal which sealed the win for France at the Gillette Stadium near Boston, before later being substituted after taking a knock to the ankle, and being replaced by Jean-Philippe Mateta.
"I'm fine. I took a knock on the ankle but I'm fine. I think at that point JP was more prepared than me to play the final 15 minutes so I came off."
He will expect to be fit for the semi-finals, with France now heading to Dallas to play the winner of Friday's quarter-final clash between Spain and Belgium. That last-four tie will take place next Tuesday, July 14.
France won their first World Cup in 1998 and their second in 2018, before losing the 2022 final on penalties to Argentina.
World Cup 2026
The 2026 World Cup will be held from June 11th to July 19th in the United States, Canada and Mexico. The tournament will feature 48 national teams and will be played in 16 modern stadiums.
Match schedule and times | Draw | England at the World Cup | Bellingham: England 'shouldn't fear anyone' | How to watch the World Cup | Predictions and odds