The seven-time champion described reports in two Italian newspapers that Ferrari were considering replacing Vasseur as “nonsense”.
Ferrari said they were not worth commenting on.
“Most people don’t know what’s going on in the background,” Hamilton said. “That’s not part of the discussion.”
He added: “I don’t think that’s on the cards as far as I’m aware and it’s certainly not something I would be supportive of.
“Embedding new people, whether it’s a driver or engineers or people who run an organisation, it takes time to adjust and the impact can be significant. That is not part of the discussion. I am here to win with Fred and he has my full support.
“I have just started with Ferrari and I am here for several years. There is no question where my head is at and what I am working towards achieving with this team. There are zero doubts.”
Vasseur joined Ferrari at the beginning of 2023 after chairman John Elkann removed his predecessor Mattia Binotto following a 2022 season that had started well but took a turn for the worse amid poor reliability, operational errors and lack of development compared with Red Bull.
Last year, Ferrari came close to winning the constructors’ title for the first time since 2008, ending the year just 16 points behind McLaren, and were expecting this season to be a close fight at the front.
Instead, McLaren drivers Oscar Piastri and Lando Norris have won seven of the first nine races, and Red Bull’s Max Verstappen is the only other driver to visit the top step of the podium with wins in Japan and Imola.
Hamilton has struggled in his first races with the team, and has generally been a little behind Leclerc.
He is one place and 23 points behind the Monegasque in the drivers’ championship.
Hamilton said: “It’s been a whirlwind of a year. Everything outside the race track is going amazing, and I am working as hard as I can to make sure that’s reflected in the results.
“We need to bring more performance to the car. We have had one upgrade in Bahrain. Hopefully soon we will have another.
“The car I am racing right now is not a car I have had input into developing and evolving over the past four years. I am driving a car Charles has been part of developing. It has its challenges but I am enjoying that challenge.”
