Two American nurses have been declared cured of Ebola, and one was healthy enough to leave hospital and meet President Barack Obama.

The good news for the nurses, who contracted Ebola while caring for a Liberian patient in Texas, came as the city of New York was dealing with its first case of the deadly virus.

Nina Pham smiled and appeared healthy, wearing a turquoise shirt and dark business suit at a news conference on Friday outside the National Institutes of Health Clinical Centre in Bethesda, Maryland.

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“I feel fortunate and blessed to be standing here today,” Pham told reporters, expressing her gratitude for those who prayed for her and cared for her while she was sick.

“I am on my way back to recovery even as I reflect on how many others have not been so fortunate.”

Pham was the first US healthcare worker to be infected with Ebola while working inside the United States, catching the disease from Liberian patient Thomas Eric Duncan, who was admitted to Texas Health Presbyterian Hospital Dallas on September 28.

Her colleague, nurse Amber Vinson, also came down with Ebola. She, too, is clear of the virus but has not yet been released from Emory University Hospital in Atlanta, Georgia.

“Tests no longer detect virus in her blood,” the hospital said, adding that she was “making good progress,” but would stay in the serious communicable diseases unit for continued supportive care until further notice.

Pham, 26, said her thoughts are with her friend, Vinson, and another American doctor, Craig Spencer, who was diagnosed with Ebola in New York on Thursday after returning from Guinea.

Pham met Obama at the White House before returning to Texas.

Pham’s Ebola diagnosis was announced on October 12, followed by Vinson’s on October 15.

Both nurses had extensive contact with Duncan, who travelled from his native Liberia to Texas to visit family last month before he fell ill and died of Ebola on October 8.

Pham and Vinson worked in the intensive care unit, though it remains unknown exactly how they were infected.

The Centres for Disease Control and Prevention said a “breach of protocol” was to blame, and has since issued stricter guidelines for donning protective gear when caring for Ebola patients.

Ebola is spread though close contact with the sweat, vomit, blood or other bodily fluids of an infected person.

On Thursday, Spencer was found to be infected with Ebola after treating patients in West Africa for the charity Doctors Without Borders.

More than 4800 people have died of Ebola so far this year, mainly in Liberia, Guinea and Sierra Leone, according to the World Health Organisation.