DALLAS (Reuters) - The family of Thomas Eric Duncan, the only person to die of Ebola in the United States, said on Wednesday it had reached a settlement with the hospital that had treated him and admitted to making mistakes in addressing his care.

The settlement includes financial support for Duncan's family but the amounts were not revealed. Texas Health Presbyterian Hospital also said it is creating a memorial fund in his honor to help Ebola victims in Africa.

"We have wrapped this up," family lawyer Les Weisbrod told reporters, adding the family will not be billed for Duncan's care. "The size and details of the settlement are confidential."

A suit against the Dallas hospital faced long odds due to the state's regulations on malpractice suits that have made it one of the hardest places in the United States to sue over medical errors, especially those that occur in the emergency room, according to plaintiffs' lawyers and legal experts.

The hospital said in a statement the settlement "serves as an example of the common-sense Texas laws that allow discussions to take place immediately and be resolved quickly."

Duncan, a Liberian national who recently arrived in the United States, first sought treatment at Texas Health Presbyterian Hospital in late September, telling staff he had been in Africa. It was later discovered that he had been in Liberia, one of three West African countries hit hardest by the Ebola outbreak.

Two days after he was discharged, Duncan had to be carted back to the same hospital by ambulance, and became the first person in the United States to be diagnosed with the virus. He was placed in an isolation unit and died 10 days after being admitted.

Two nurses who treated Duncan, Nina Pham and Amber Vinson, both contracted Ebola but recovered. The settlement will provide financial support for Duncan's four children, his mother, Nowai Korkoyah, who lives in North Carolina, and his father, Jacob Duncan, who lives in Liberia.

The hospital had previously apologized to Duncan's family for not being able to save his life and said it made a mistake by initially discharging him. The Ebola outbreak has killed more than 5,100 people this year, most of them in Guinea, Liberia and Sierra Leone.

By Lisa Maria Garza

(This version of the story corrects sixth paragraph to say Duncan told hospital staff he had been in Africa, not Liberia) (Writing by Jon Herskovitz; Editing by Doina Chiacu, Bill Trott and Jim Loney)