Bob Odenkirk is said to be in a "stable" condition in hospital after collapsing on the set of Better Call Saul on Tuesday.
The 58-year-old was recording scenes for the final season of the Breaking Bad spinoff when he fell ill in what is being described as a "heart-related incident".
A statement from the actor's representatives said: "He and his family would like to express gratitude for the incredible doctors and nurses looking after him, as well as his cast, crew and producers who have stayed by his side.
"The Odenkirks would also like to thank everyone for the outpouring of well wishes and ask for their privacy at this time as Bob works on his recovery."
US network AMC, which airs the show, said: "Bob is someone we have known and been lucky enough to work with for a long time.
"The immediate outpouring of affection and concern from fans around the world is a clear reflection of his immense talents and ability to both move and entertain people.
"Like everyone else, we are so grateful to know he is in stable condition and receiving excellent care. We are holding him close in our thoughts and wishing for a fast and full recovery."
The final, 13-episode season of Better Call Saul is due to premiere early in 2022.