Ocaranza said he still urges residents to receive a vaccine.
City officials didn't say which vaccines the people who died had received.
"The fact that we're seeing a very small number of breakthrough cases doesn't mean that we need to lose faith in the vaccines," Ocaranza said. "If we compare the era before the vaccine to now that we have the vaccine, the number of people hospitalized because of COVID has dropped tremendously."
El Paso close to herd immunity against COVID-19
The city of El Paso reported 46 new positive cases Wednesday as the city and county inch closer to achieving herd immunity against COVID-19. It also reported five more deaths, raising the total to 2,693. There are 687 active cases, with 50 people hospitalized, including nine in intensive care.