The condition of a Liberian with Ebola, being treated with an experimental drug at a Texas hospital has slightly improved, though he remains critical, hospital officials said Tuesday.

Thomas Eric Duncan was the first person diagnosed with the deadly Ebola virus outside of Africa, though he is believed to have become infected in Liberia.

On Monday, he started receiving an experimental treatment called brincidofovir, the first time the medicine has been used to fight Ebola in humans.

“Mr. Duncan remains in critical condition. His condition is stable,” said a statement from Presbyterian Hospital in Dallas.

“His liver function, which declined over the weekend, has improved, but doctors caution that this could vary in coming days,” it said.

He is on a ventilator and receiving kidney dialysis, the hospital added.

Duncan will continue to receive the experimental drug, which is manufactured by the North Carolina-based pharmaceutical company Chimerix.

The drug has been tested in about 1,000 people against adenovirus and cytomegalovirus and prevents viruses from creating copies of themselves, according to Chimerix.

Of the 48 people under observation, 10 are deemed to be at high risk, officials said. Three of those people shared an apartment with Mr. Duncan and seven are health care workers. The other 38 people are considered to be at lower risk.

“None of them is sick, none of them has a fever,” Dr. Thomas R. Frieden, the director of the C.D.C., said Tuesday.

Dr. Frieden said Mr. Duncan’s condition and the lack of new cases were positive signs with implications for what he said will be a long fight against the disease.

There is no approved treatment for Ebola and no vaccine against the virus.

But two prototype vaccines have been earmarked for Phase I trials, the first step in the three-pronged process to vet a new drug for safety and effectiveness.

The current Ebola outbreak in West Africa is the deadliest in history, and has already killed nearly 3,500 people.

President Barack Obama said the chances of a widespread Ebola outbreak in the United States were “extraordinarily low,” but pressed world leaders to ramp up the fight against the virus.