It was confirmed earlier this week by Morrison that Taylor, 78, was admitted to the hospital after suffering symptoms from congestive heart failure.
Morrison did not offer details of the treatment and did not know exactly how long Taylor would be in the hospital.
"She had a pretty good day Saturday, and a good night," Morrison said today. "At this stage, with her history, they're going to want to keep her in for a while just to make sure they've fixed what they needed to fix."
Previously Morrison expressed appreciation for concern from Taylor's fans, but requested privacy for her client while she is being treated.
"Her family and close friends are appreciative of the warm support and interest of her loyal fans but have asked that people respect her privacy and allow her medical team the time and space to focus on restoring her back to health," Morrison said in a written statement.
Late Thursday evening, Morrison denied a tabloid report that the screen legend was rushed to the hospital with intense abdominal pain.
"Ms. Taylor was hoping to attend the 25th Anniversary event of AmFAR last night [Wednesday] where she was honored by the organization," read an e-mail to ABC News Thursday on behalf of Morrison.
"Unfortunately, the combination of the unstable weather conditions and the fact that she was feeling under the weather forced her to make the decision not to travel. A message from Elizabeth was released at the AmFAR event last night.
"It seems that the combination of her non attendance last night, combined with the fact she was photographed last week leaving her dentist's office in a wheelchair, has caused a lot of negative speculation," the statement added. "Thanks for your concern."