A Texas health worker who may have had contact with specimens from the first patient diagnosed with Ebola in the United States has been isolated on a cruise ship despite showing no symptoms of the disease, the Department of State said on Friday.

The Texas Health Presbyterian Hospital worker, who did not have direct contact with now deceased Liberian patient Thomas Eric Duncan but could have processed his bodily fluids 19 days ago, left on a cruise from Galveston on Sunday, department spokeswoman Jen Psaki said in a statement.

U.S. concerns have intensified after two nurses from the Dallas hospital who cared for Duncan contracted the virus, which has killed nearly 4,500 people, mostly in West Africa. President Barack Obama's administration is facing sharp criticism from lawmakers over its efforts to contain the disease at home.

The employee has been self-monitoring since last Monday and has yet to develop a fever or show any other symptom of Ebola, the statement said. The worker and a companion voluntarily isolated themselves in their cabin, and U.S. officials are arranging for the ship to return to the country.

"We are working with the cruise line to safely bring them back to the United States out of an abundance of caution," Psaki said in the statement.

The person left the country before being notified of the U.S. Centers for Disease Control and Prevention's (CDC) updated requirement for active monitoring, the statement said.

The Government of Belize said in a statement hours earlier that it had denied a request by U.S. officials to use a Belizean airport to transport a cruise ship passenger considered to be a very low risk for Ebola.

"The passenger never set foot in Belize," the statement said. "When even the smallest doubt remains, we will ensure the health and safety of the Belizean people."

The maximum incubation window for the disease is 21 days, according to the CDC.