The Foxes have lost their last seven Premier League games and are second bottom, two points from safety, following a 2-0 defeat by Fulham.
Van Nistelrooy, who replaced Steve Cooper in November, has won only two of his 10 games in all competitions, including a 6-2 FA Cup victory over QPR.
"I'm focused on getting this team out of the situation, that's my only concern," he said to reporters.
"I'm with the players, working with everyone at Leicester to get the best out of this squad, and in difficult times. In tough times, you need to be strong, show character, work and persist and be committed.
"We are united and committed. That is the spirit and you can see that on the pitch. I can see a team with spirit and fight. If we continue this run will end."