(CNN) A large majority of Americans, 71%, say they will "definitely or probably" get a Covid-19 vaccine, according to a survey out Tuesday from the Kaiser Family Foundation.
That's up from 63% in September - indicating a steady increase in trust as regulators worked to authorize the vaccine and held public meetings to discuss data supporting their use.
But Black Americans, people living in rural areas and Republicans are more hesitant about getting the shots.
A third of those surveyed said they want to get a vaccine "as soon as possible," and 39% of those surveyed said they would "wait and see" how initial vaccination goes before getting a vaccine themselves.
The non-profit health research group surveyed 1,676 adults for the survey, which the group is launching as the Covid-19 Vaccine Monitor and plans to update regularly.
The US Food and Drug Administration gave emergency use authorization to Pfizer's Covid-19 vaccine last week after a public meeting of its independent advisers. The Centers for Disease Control and Prevention supported the EUA after a public meeting of its own advisers over the weekend.
Vaccines rolled out to all 50 states Monday and many doctors, nurses and other staff stepped up to get publicly vaccinated..
But officials say they are worried that many Americans still mistrust such a new vaccine.
The survey indicated a small hard core of vaccine skeptics.
About 15% said they would "definitely not" get a Covid-19 vaccine. "This group is disproportionately made up of Republicans and of people with no more than a high-school level education," Kaiser said in a statement.
Just 9% of those surveyed, mostly essential workers, reported they would get a vaccine only if it were required by work, school, or other parts of their lives.
"What's interesting is if you dig into the reasons for hesitancy among different groups you see that they really differ depending on who you're talking to," Liz Hamil, director of Kaiser's public opinion survey research program, told CNN.
The survey also looked at motivations behind vaccine hesitancy, and found that the groups that are the most vaccine hesitant are Republicans, 30 to 39-year-olds, rural Americans, and Black Americans.
"Some Black adults are hesitant for reasons that could change with more information. For example: 71% of those who say they won't get vaccinated say a major reason is that they are worried about possible side effects (which are expected to be mild) and half (50%) say they worry they could get COVID-19 from the vaccine," KFF said.
That's "kind of a warning sign of potential misinformation spread among that group," Hamil said.
Both African Americans and Latinos expressed concern over how the vaccine development process was taking their needs into account. Only 11% of African Americans and 16% of Latinos were "very confident" that the process was taking their needs into account.
For Republicans, 57% of those surveyed chose "the risks of Covid-19 are being exaggerated" as a major reason they definitely or probably would not get a vaccine.
"Many Americans who are hesitant are simply reserving judgment before they are ready to get vaccinated. However, nearly one in four Republicans don't want to get vaccinated because they don't believe COVID poses a serious threat," said Mollyann Brodie, executive vice president with the Kaiser Family Foundation. "It will be a real challenge to undo COVID denialism among this slice of President Trump's political base."
Those surveyed were asked to rate their level of enthusiasm about the vaccine—if they would get the vaccine as soon as possible, wait and see how it's working, only if it was required for school or work, or definitely not get it.
The Kaiser team found 39% of participants fell into the "wait and see" group. About half, 52%, of Black Americans fell into this group; 43% of Latinos did and 36% of Whites. Whites made up 40% of the "as soon as possible group," but only 20% of Blacks and 26% of Hispanics said they wanted a coronavirus vaccine right away.
"Based on our data, what happens in this initial rollout is going to be critically important in both how smoothly it rolls out but also how those reports get filtered out to the media, and what people's different media sources are telling them about how that that initial rollout goes," Hamil said.
"It's a lot more difficult because it's not like a single national ad campaign with one national trusted messenger who can get out there and make people trust this. It's really going to be an army of on the ground messengers," she said.
Kaiser asked participants who they trust the most to get their information. An overwhelming number, 85% said they trusted their personal health care providers over everyone else, and that includes national, state and local messengers. The Centers for Disease Control and Prevention, local health departments, the Food and Drug Administration and Dr. Anthony Fauci were all considered more trusted sources of information than President Trump, who was ranked the least trusted messenger, chosen by 34%.
"We've seen throughout the course of the last few months, you know, trust eroding and becoming more partisan as these different groups and potential messengers have gotten tied up in political discourse," Hamil said.
The study also found that a large majority of Americans believe that the vaccine will be widely available by next summer, that more people are confident that the vaccine will be properly tested before being administered.
Those surveyed also now believe that the vaccine will be distributed fairly as it becomes more available. This increase was most pronounced among African Americans -- only 32% were only confident in equitable distribution of the vaccine in September, but that share is now up to 62%.