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."
Taylor is a two-time Academy Award-winning actress, who in later life became notorious for her multiple marriages and sometimes eccentric behavior. She has reported health problems in recent years and appeared frail in public appearances.
However, she was well enough to have a conversation with reality star Kim Kardashian that has been published in Harper's Bazaar. In fact, on Wednesday, Taylor touted the newly published article on her Twitter feed.
"Our interview in Bazaar came out!" she wrote. "You look like a princess in Egyptian robes, love!"
In the interview, she talked about her love life, her iconic roles and her jewels.
"I never planned to acquire a lot of jewels or a lot of husbands," Taylor said. "I have been supremely lucky in my life in that I have known great love, and of course, I am the temporary custodian of some incredible and beautiful things."
Taylor also mused about one of her seven former husbands, actor Richard Burton.
"It was inevitable that we would be married again, but it's not up for discussion," she said.
Taylor reported in October 2009 that she was having a heart procedure done. Via Twitter, she announced that it was "very new and involves repairing my leaky valve using a clip device, without open heart surgery so that my heart will function better."
Elizabeth Taylor's Long History of Health Ailments
In her seven decades, Taylor has had her share of medical problems, debilitating conditions, painful injuries and freak accidents. These included a fall from a horse during one of her early film shoots, bouts with pneumonia and skin cancer, a tracheotomy, treatment for alcohol and painkiller addictions, and lung, hip, brain and heart surgeries.
She has undergone anywhere from 30 to 40 surgeries, according to biographers.
In addition, she has seen her dramatic life frequently covered by gossip magazines, which have frequently documented evident fluctuations in her weight over the years.