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WATCH: Florida governor gives coronavirus update amid rise in cases

Florida Gov. Ron DeSantis held a briefing on the surge in COVID-19 cases in the state.

Watch the governor’s remarks in the player above.

The increase in coronavirus cases has filled some Florida hospitals, or brought them close to their capacity.

Florida recorded more than 12,000 new confirmed coronavirus cases Monday after a record-setting weekend, a spike that partly reflects the large number of tests being performed.

The state reported 12,624 new cases out of more than 112,000 tests reported since Sunday, when the state reported 15,300 new cases, a national record.

The state has seen a positivity rate for tests of just over 11% the last two days. That is still four times the 2.3% rate the state had in late May, but a drop from the near 20% rate seen last week. Officials have said they want to get the rate below 5%.

The state added another 35 deaths Monday, with the one-week average remaining at 71 per day.

The daily rate had been 30 deaths three weeks ago, and crept up to 44 last week before skyrocketing with a state record 120 deaths reported Thursday.

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