Ferrari chairman John Elkann says the company has "full confidence" in team principal Frederic Vasseur.
The Italian team have had a difficult season and are in danger of slipping to fourth in the constructors' championship after being as high as second earlier in the year.
Lewis Hamilton gave them their only victory this year when he won the sprint race at the Chinese Grand Prix, the second race of the season.
Elkann's comments come in the wake of a report claiming that Ferrari had been talking to former Red Bull team principal Christian Horner about taking over from Vasseur.
He said: "I want to express our full confidence in our team principal, Fred Vasseur, and in the work he is carrying out together with all our colleagues at Scuderia Ferrari — the mechanics, engineers, and drivers competing this weekend in Austin.
"I also want to reaffirm the importance of teamwork by everyone to maintain focus on the only goal that matters: always giving our very best on the track."
Elkann spoke before being given a prize at an event in Washington DC to mark the 50th anniversary of the National Italian American Foundation.
Vasseur, who has been in his role since January 2023, was given a new contract by Ferrari two and a half months ago.
Hamilton said on Thursday at the United States Grand Prix in Austin that the stories about Horner and Ferrari were "distracting".
Elkann's comments came after Ferrari issued guidance implying there was no truth to the Horner claims.
In Saturday's sprint race in Austin, Hamilton finished fourth with team-mate Charles Leclerc fifth.