New York Governor Andrew Cuomo speaks during a press conference to discuss the first positive case of novel coronavirus or COVID-19 in New York State on March 2, 2020 in New York City.

New York Gov. Andrew Cuomo confirmed that a family of four and their neighbor have tested positive for the coronavirus, bringing the number of cases in the state to at least six.

New York officials identified the father as the state's second case, which was confirmed Tuesday. Cuomo said the patient's 20-year-old son and 14-year-old daughter tested positive for COVID-19. The patient's wife, Cuomo added, and a neighbor who drove the father to the hospital have also tested positive.

The patient is at New York Presbyterian Hospital and in critical condition, the NYC Health Department said Tuesday.

"We have an epidemic caused by coronavirus, but we have a pandemic that is caused by fear," Cuomo said at a press conference Wednesday. "There are going to be many, many people who test positive."

The new cases bring the total confirmed in the state to six, including a health-care worker who returned from Iran and was identified as the state's first COVID-19 patient on Sunday.

The family of four lives in Westchester County. The father works at the Manhattan law firm Lewis and Garbuz, P.C., the health department said Tuesday. Both of his children attend school in the city. His son attends Yeshiva University in Manhattan, while his daughter goes to SAR Academy and High School in the Bronx. SAR Academy voluntarily closed Tuesday as a precaution. Yeshiva University canceled classes Wednesday at its Wilf campus in Washington Heights, saying in a statement it was "taking every precaution.

Cuomo said he is meeting later Wednesday with officials in Westchester to make a plan to identify and test people who might have come into contact with the new patients.

New York Mayor Bill de Blasio said city "disease detectives" were on campus to identify and track close contacts and get them immediately tested. Two people have been transferred to Bellevue hospital for testing, he said.

The virus has now infected 108 people across the U.S., according to the Centers for Disease Control and Prevention, and killed nine, all in the Seattle area. New York officials confirmed Sunday the state's first coronavirus case, a woman who recently traveled to Iran and is currently isolated in her Manhattan home.

"This appears to be an example of community spread," de Blasio said at a news briefing Tuesday, meaning the virus is being spread within the community without any known links to people who were confirmed to have caught it overseas or directly from one of those travelers.

"Go on with your lives," de Blasio said Tuesday. "Go on with your business."

Read CNBC's live updates to see the latest news on the COVID-19 outbreak.