Officials with public health departments in Harris County and the city of Houston confirmed 241 new cases of COVID-19 June 3 as well as five deaths attributed to the coronavirus.

Total cases have risen to 13,268, 7,812 of which are considered active while 5,215 are confirmed to have recovered. A total of 241 people are confirmed to have died from the coronavirus in the county.

The updates came on the same day Texas Gov. Greg Abbott announced plans for Phase 3 of reopening businesses in Texas, including plans to allow almost all businesses to start operating at 50% occupancy. In a statement, Abbott said 45% of new cases statewide between May 26 and June 2 can be tied to prisons, jails, meat packing plants or nursing homes.

"Thanks to the effectiveness of our Surge Response Teams, we have the ability to contain those hot spots while opening up Texas for business," Abbott said. "As we begin Phase III, I ask all Texans and Texas businesses to continue following the standard health protocols and to heed the guidance of our state and federal officials who continue to closely monitor COVID-19. If we remain vigilant, we will continue to mitigate the spread of this virus, protect public health, and get more Texans back to work and their daily activities."

Harris County hospitals rates have remained steady, with about 45% of general beds and 88% of intensive care unit beds occupied as of June 1, according to data being tracked by the Southeast Texas Regional Advisory Council.

Of the 1,628 operational ICU beds, about 1,434 were occupied on June 1, down from a recent high of 1,477 on May 29. Another roughly 300 ICU beds exist in surge capacity in the county, according to SETRAC.