Bob Odenkirk was rushed to the hospital on Tuesday after he collapsed on the New Mexico set of the AMC series

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After suddenly collapsing on the set of Better Call Saul on Tuesday, Bob Odenkirk is in "stable condition," his rep tells PEOPLE.

Odenkirk, 58, was rushed to the hospital Tuesday morning after collapsing on the New Mexico set of the beloved AMC series, which is currently in production on its sixth and final season.

"We can confirm Bob is in stable condition after experiencing a heart related incident," Odenkirk's reps tells PEOPLE in a statement. "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," the statement continues.

Also on Wednesday, Odenkirk's son, Nate, tweeted a message to fans seemingly about his father. "He's going to be okay," the tweet read.

TMZ reported that Odenkirk is currently recovering in an Albuquerque hospital.

Sources told the outlet that he was unconscious during the early hours of his stay there, but is now lucid.

Many of Odenkirk's famous friends have sent their well-wishes on social media, including Breaking Bad stars Bryan Cranston and Aaron Paul, Elijah Wood, David Cross, and Michael McKean, who plays Odenkirk's brother on Better Call Saul.

Better Call Saul Season 3
Bob Odenkirk in Better Call Saul
| Credit: Michele K.Short/AMC/Sony Pictures Television

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Odenkirk stars as lawyer Jimmy McGill/Saul Goodman in Better Call Saul, which takes place before the events of Breaking Bad. He's been nominated for four lead actor Emmys for the role.

The actor previously won two trophies for writing on Saturday Night Live (1989) and The Ben Stiller Show (1992).

Better Call Saul had just begun production on its final season in April, Odenkirk previously told James Corden on The Late Late Show with James Corden, though it's unclear how much filming time on the season remains.

"I know as I get closer to the end of it, I'm going to have to somehow reconcile with saying goodbye to this gift that I got from the universe. It's hard to take into account how much it brought into my life," Odenkirk told Corden at the time, adding that playing Goodman had "changed" his life.