Mayor Jenny Wilson apologized on Twitter.
"We recognize our system for scheduling failed and are working to address. We apologize. Please stand by," she wrote.
Multiple people called 2News to report the system was not working or that they had issues signing up.
The Salt Lake County Health Department said in a statement that the website could not handle the tens of thousands of people who were trying to sign up.
As of 10:00 a.m., 15,042 individuals had successfully registered.
“We are very sorry for this problem. The health department estimates there are approximately 70,000 Salt Lake County residents 70 and over. The health department has 30,000 appointments available through February 27. That number of appointments is based on the number of doses we have been told we can expect to receive,” Wilson said in a statement.
The department reportedly is working to prevent any such problems from happening in the future.
Residents of the county, who are 70 years and older, were eligible to sign up for a vaccination appointment Wednesday at 8 a.m. Residents can also call, but hold times may be possible.
Those who get an appointment will be signed up for vaccinations next week at the Mountain America Expo Center in Sandy.
Vaccines are limited, even with a few thousand coming to Salt Lake next week. Those will be divided among priority groups, including seniors, teachers, health care workers and first responders.
For more information, visit: slco.org/health/COVID-19/vaccine
The health department said those who sign up and don't receive an email confirmation should email lmmsSuppport@slco.org.