Rick Cotton, the executive director of the Port Authority of New York and New Jersey, has tested positive for coronavirus, Gov. Andrew Cuomo on Monday said. 

Cotton is working from home, as are his top staffers who are being tested. 

Cuomo, at a news conference providing an update on the spread of the virus, said he himself has not been tested for the virus. 

"The truth is we don't have the testing capacity," Cuomo said. "We can't test people on that kind of whim."

Cotton is in charge of managing the ports and borders in New York, including bridges, airports and other key points of entry in the state.

At maximum, the state will be able to do tests for "several thousand" people as the process ramps up. Cuomo is seeking automatic testing approval from the federal government and spoke with Vice President Mike Pence about the issue. 

"I am not a probable positive," Cuomo said. "We are looking for the probable positives."