DALLAS (CBSDFW.COM) – Almost 2,000 hospital beds are empty and available in Dallas, but city leaders worry that may not be enough to handle the rapidly increasing number of COVID-19 patients needing to be hospitalized.

“COVID-19 is spreading rapidly in Dallas County,” warned Dallas Mayor Eric Johnson.

READ MORE: 16-Year-Old Shot To Death Outside Hurricane Harbor In Arlington

He plead with the public to follow the recommendations of medical experts.

“Wear a mask,” he urged repeatedly during a news conference Wednesday.

Dallas Mayor Eric Johnson (CBS 11)

Data from the Department of State Health Services shows hospital beds in Texas filling up, nowhere more than in the Houston and Dallas-Fort Worth regions.

Parkland Hospital says 85% of its beds are now occupied.

READ MORE: Community Groups Want To Help Reduce Violent Crime In Dallas

Ninety-three of its hospitalized patients, or roughly 1 in every 8, are currently assigned to a COVID-19 bed.

A hospital spokesperson said it would add another 48 beds for COVID-19 patients by Friday.

“We want to make sure that we’re not in a position where we don’t have the hospital beds and ventilators to take care of our people,” said Mayor Johnson.

The mayor said representatives from the city, county, and DFW Hospital Council will meet Thursday to discuss whether to prepare the Kay Bailey Hutchison Convention Center to serve as a temporary medical facility.

“There is a great deal of concern in Texas about ICUs filling up and about them reaching their capacity to take care of patients,” said Dr Susan Bailey, president of the American Medical Association and Fort Worth physician.

She said everyone should assume it is their personal responsibility to help control spread of the virus.

MORE NEWS: Eye On Culture: Dallas Holocaust And Human Rights Museum Fulfilling Its Mission To Educate

“Regardless of the cause the only way we know that works to fight this is to wear a mask, wash your hands, and keep your distance,” she said.