PITTSBURGH (AP) _ A 2-year-old girl with liver failure whose family's appeal for a donor organ drew presidential support died today before a liver could be found for her, hospital officials said.

Kimberly Izzo, daughter of Alfred and Lois Izzo of Woodbridge, N.J., died of liver failure at 5:30 a.m. at Children's Hospital of Pittsburgh, said hospital spokeswoman Mary Ann Ference.

''No additional details will be released at this time at the request of the family,'' Miss Ference said.

The girl, who was admitted to the hospital Tuesday, did not receive a new liver despite being given a high priority for a new organ of her size and age, said hospital spokeswoman Lynn McMahon.

Izzo received a telegram from President Reagan only about four hours after he called the White House on Friday and spoke to a presidential assistant, he told reporters before his daughter's death.

''Nancy and I have learned about little Kimberly and her need for a liver transplant. Keep your faith strong and your hopes high. Americans are generous people and will give the gift of life once they know the needs of others such as Kimberly,'' the telegram read, according to hospital spokeswoman Carole Adzent.

''I have often urged Americans to become organ donors and do so once again. May God Bless You, Ronald Reagan,'' the message concluded.

White House spokesman Ben Jarrett confirmed Sunday that Reagan sent the telegram.

Kimberly was a normal, healthy child until two weeks ago, when she came down with an infection that attacked her liver, Miss McMahon said. She was in critical condition in the hospital's intensive care unit for several days.

Miss McMahon said doctors did not identify the cause of the infection.

Izzo said Reagan's telegram ''itself meant nothing to me, but I took it and I read it on the (television) news. It's not as good as if Reagan were to read it himself. ... I just hope that if the president is involved it will generate some response,'' he said before Kimberly's death.