Kentucky will pick up the pace of COVID-19 vaccinations, Gov. Andy Beshear pledged Monday as he announced more than 2,300 new coronavirus cases and 26 more virus-related deaths.

The statewide rate for positive COVID tests surpassed 11% and more than 1,700 Kentuckians are hospitalized because of the virus — more troubling signs in the fight against the pandemic.

To accelerate inoculations, the goal is for every vaccination site to administer at least 90% of all vaccine within a week of receiving it, said Dr. Steven Stack, Kentucky’s public health commissioner.

“The goal is to not have vaccine sitting in a freezer,” Stack said at a news conference. “The goal is to have vaccine administered to willing recipients.”

Beshear expressed dissatisfaction with the vaccination pace since the shots started late last year.

“We have too many people out there that are rightfully anxious, and they need to see this whole country pick up the pace,” the governor said. “We’re certainly going to do it here in Kentucky.”

As of Sunday, more than 60,400 vaccine doses had been administered in Kentucky out of more than 174,700 doses received, he said. Residents and staff in long-term care facilities along with frontline health care workers are at the top of the list for receiving those vaccinations.

About 57,000 more doses will be delivered to Kentucky this week, Beshear said.

The plan to accelerate statewide vaccinations will include “building up larger operations that we can get more people through,” the governor said.

Health care workers along with residents and staff at long-term care facilities are in the top tier for vaccinations. The next tier targets emergency responders, K-12 school personnel and people 70 and older, with the goal of starting those vaccinations by early February.

The next vaccination group includes people 60 and older, anyone older than 16 with high-risk medical conditions and anyone deemed an essential worker. The next tier includes people ages 40 and older, followed by another broad category of people ages 16 and older.

While people in the highest categories will be prioritized, there could be instances when people in lower tiers get vaccinated sooner to ensure that the vaccine is being administered.

“The goal is not to have it wait and hang over ’til the next week,” Stack said. “It’s to administer it and use it. And then when you get the next shipment, start over again with that process.”

Meanwhile, Beshear reported 2,319 new coronavirus cases Monday, as the statewide total surpassed 279,000 cases since the start of the pandemic. The 26 latest deaths included people ranging in age from 40 to 102 and raised the state’s virus-related death count to at least 2,749.

Among the more than 1,700 virus patients hospitalized in Kentucky, more than 450 are in intensive care, Beshear said. The statewide rate for positive tests reached 11.2%.

For most people, the coronavirus causes mild or moderate symptoms that clear up within weeks. But for others, especially older adults and people with existing health problems, the virus can cause severe symptoms and be fatal. The vast majority of people recover.