Tracy Morgan Had Leg Surgery, Does Not Need Amputation: Rep

Tracy Morgan in 2013

Bobby Bank/WireImage

updated 06/09/2014 AT 4:00 PM ET

originally published 06/09/2014 AT 8:20 PM ET

Rumors that Tracy Morgan’s leg is being amputated are false, his rep said Monday.

“Tracy remains in critical but stable condition. His fiancée Megan is by his side,” according to a statement to PEOPLE. “As we shared yesterday, Tracy had surgery on his broken leg.”

Morgan, 45, was injured early Saturday after the limo bus he was riding from a stand-up show in Delaware was struck by a truck in a six-vehicle accident. He is being treated at Robert Wood Johnson University Hospital in New Brunswick, New Jersey.

Friends, family and fans have rallied around the former SNL and 30 Rock star, who is expected to remain hospitalized for several weeks.

“This recovery will be arduous and we hope that you can be patient during this difficult time,” his rep’s statement continues.

The wreck hurt two others and killed comedian “James.

Walmart truck driver Kevin Roper, who police say hadn’t slept in more than 24 hours before getting behind the wheel, faces one count of death by auto and four counts of assault by auto.

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