(HealthDay News) — In another sign that COVID-19 vaccination rates have plateaued in America, a new poll shows that most adults who wanted a COVID-19 vaccine have already gotten one.

Released Wednesday, the Kaiser Family Foundation report shows 65% of adults polled have received at least one dose of the vaccine, up from 62% in May. But only 3% of those who have not been vaccinated said they plan to do so as soon as they can. About 14% said they will definitely not get vaccinated.

Nearly 20% of the people who are not vaccinated said they believe the vaccine is too new. A smaller number of people surveyed cited other reasons, like concerns about side effects or distrust in the government. More than 30% of adults who are not immunized said they would be more inclined to get a vaccine if it is completely approved by the U.S. Food and Drug Administration. All COVID-19 vaccines in the United States are now only approved for emergency use.

The report did uncover one bright spot: When employers encourage vaccination, rates rise. About 73% of workers with employers encouraging COVID-19 vaccination said they have received at least one shot, compared with 41% with employers not encouraging vaccination.

The report also found that in most American households, either everyone is vaccinated against COVID-19 or no one is. The poll shows 77% of vaccinated adults said everyone in their home is vaccinated, whereas 75% of unvaccinated adults said no one they live with is. But overall, more people live in vaccinated homes: 50% of adults said they live in fully vaccinated households, whereas 25% said they are in fully unvaccinated households, the poll showed.

KFF COVID-19 Vaccine Monitor