Les Bleus have won just once so far this tournament, a narrow win at Scotland, sandwiched between a humbling at home to Ireland and Sunday's 13-13 draw with the Azzurri in Lille.
Galthie's out-of-form outfit still seem to be suffering after October's Rugby World Cup quarter-final defeat to South Africa in Paris.
"I'm a manager, I'm not the type of person to make swift changes due to pressure," Grill told AFP.
"It's not a decision made based on one game, one point and not on a transition period of matches that are difficult.
"Fabien Galthie is absolutely not under pressure," Grill added.
Since the heartbreaking World Cup exit, 54-year-old Galthie has replaced influential, experienced members of his coaching staff with lesser-known individuals and has had to deal with the absence of numerous key players.
Regular captain and scrum-half Antoine Dupont is away with the France seven-a-side team preparing for this summer's Paris Olympic Games. First-choice players like lock Thibaud Flament, Anthony Jelonch and Romain Ntamack have missed the start of the Six Nations through injury.
"You have to realise the reality of the quarter-final, in France, with all the pressure around it," Grill said.
"You have to respect the human beings. There's a big transition period to manage, it's not done overnight.
"You have to give them time, the message is resilience, solidarity, work," he added.
Galthie's reluctance to accept the difficult situation and his team selections have been the basis of much criticism from fans, the media and former players.
Since June 2023, Galthie, who has a contract until 2027, has worked alongside vice-president in charge of high-performance Jean-Marc Lhermet at the FFR.
Former Clermont director of rugby Lhermet came into the federation alongside Grill, who took over the role of FFR chief formerly held by the disgraced Bernard Laporte.
"I have full confidence in Jean-Marc and Fabien to advance, as a team and in the players," Grill said.
Next up for France is March 10th's Six Nations trip to Wales before they end the campaign by hosting England in Lyon six days later.
