An electrician sets up wiring while workers drive excavators at the construction site of a field hospital on January 24, 2020 in Wuhan, Hubei Province, China.

President Donald Trump thanked Chinese President Xi Jinping for his country's handling of the coronavirus, shortly after American health officials confirmed a second case of the flu-like virus in the United States.

"China has been working very hard to contain the Coronavirus," Trump wrote in a post on Twitter. "The United States greatly appreciates their efforts and transparency. It will all work out well. In particular, on behalf of the American People, I want to thank President Xi!"

Experts have said that the Chinese response to the outbreak of coronavirus, which was first diagnosed late last month, has been more robust and transparent than the country's handling of the SARS outbreak, which it sought to conceal in late 2002 and 2003.

The death toll escalated to dozens on Friday, authorities in the country said, with more than 800 known cases on the mainland. As part of the response, authorities were rushing on Friday to complete construction of a new 1,000-bed hospital in Wuhan, the city where the outbreak began.

The U.S. Centers for Disease Control and Prevention reported the first instance of the virus in the United States earlier this week. There are 63 cases being monitored across 22 states, according to the National Center for Immunization and Respiratory Diseases.

The second patient diagnosed with the virus is a woman in her 60s who recently returned from Wuhan, health officials said Friday. The first U.S. patient, whose diagnosis was confirmed on Tuesday, had also recently traveled to Wuhan.

In an interview on Wednesday, Trump said that he believed the virus was under control. He also said he had confidence in the Chinese government to be transparent.

"We have it under control. It's going to be just fine," Trump told CNBC's Joe Kernen.

The major stock market indexes declined on Friday amid fears that the virus could damage global growth.