Reports on Monday suggested Bilic was set for crisis talks with Sullivan and fellow owner David Gold following Saturday's humiliating 5-1 home defeat against London rivals Arsenal.
The loss left West Ham, who have won just three league matches this season, languishing only one point above the relegation zone.
Bilic's post-match verdict on his players was damning as the Croatian accused some of them of lacking dedication in training.
But Sullivan made it clear the former West Ham defender will be given time to improve the situation.
"I saw Slaven's comments after the game and as always he was completely honest with his assessment," Sullivan told West Ham's website.
"Slaven cares passionately about the football club and this defeat will be hurting him as much as anyone.
"I have no doubts that he is doing everything he can to address the situation and everyone is working together to ensure we turn our season around.
"We cannot forget the amazing job that Slaven did in his first season at the club. With a bit more luck he could have taken us into the top four.
"His passion, commitment and outstanding track record at the highest level were among the many reasons we appointed Slaven in the summer of 2015.
"Despite what some people have said, there is still a great spirit among the players and everyone is working towards the same objective."