Ferrari chairman John Elkann publicly urged both Hamilton and Charles Leclerc to “talk less and focus on driving” following a disappointing race in Brazil earlier this month.
Hamilton has described his season as a “nightmare” and has not achieved a podium finish in 21 Grand Prix races, a first in his F1 career.
Elkann's comments came as Ferrari dropped to fourth in the constructors' championship, despite acknowledging improvements in the team's mechanics and car.
Hamilton trails his teammate Leclerc by 66 points in the world championship standings, with two races remaining after this weekend’s Las Vegas Grand Prix.