By Christina Maxouris, CNN

(CNN) -- States across the US are now seeing a decline in coronavirus cases, a US top official said this week, though he warned things could quickly change again if Americans aren't careful.

Trends are now "going in the right direction," Adm. Brett Giroir, the Trump administration physician overseeing US coronavirus testing, said Wednesday during a telebriefing. He attributed the decline in part to safety protocols such as masks and social distancing.

The daily average number official new coronavirus cases reported in the US has been declining for weeks. Cases over the past week averaged about 47,300 as of Wednesday, down from a peak average of 67,317 on July 22, according to Johns Hopkins University data.

State leaders who have reported a leveling of new cases also attribute it to adherence to safety guidelines. In Washington state, where health officials say the rate of new cases is slowing, "face coverings have made a difference," Secretary of Health Dr. John Wiesman said.

Twelve states' average daily cases have risen at least 10% against the previous week, including Hawaii, Johns Hopkins data show. Hawaii's state capital dramatically tightened restrictions on gatherings -- both indoors and outdoors -- in an effort to control a surge of cases.

Despite the hopeful signs, now isn't a time to ease measures, Giroir cautioned.

"This could turn around very quickly if we're not careful," Giroir said. "We saw that early on after Memorial Day and the couple weeks afterward that sort of started the current outbreak."

The country had seen cases surge from mid-June into late July, after states lifted restrictions to curb the spread of the virus. In response, more than half the country halted reopening plans and enacted new measures to slow a spread that experts said was out of control.

Though case rates have dropped in recent weeks, daily deaths -- which experts say can spike weeks after a jump in new cases -- have recently been at a relatively elevated level.

The country's seven-day average for daily Covid-19 deaths has been above 1,000 for 24 straight days as of Wednesday, after seven weeks of below 1,000.

The seven-day average of test positivity rates in the US dropped to 6.3% as of early Thursday, down from 8.5% in mid-July, according to the Covid Tracking Project.

The director of the US Centers for Disease Control and Prevention has suggested communities' positivity rates should be below 5% to comfortably reopen schools. At least 26 states averaged above 5% as of Wednesday.

US leaders appealed to young people to skip social gatherings and practice safety guidelines. Younger groups, experts said, helped drive the rise in cases over the summer. As they head back to college campuses now, universities have already reported hundreds of positive tests.

Texas, Mississippi and Georgia report most new infections per capita across a week

Meanwhile, states across the South and West continue to report the most daily infections when adjusted for population.

Texas led the country per capita with the most average cases per day over a week as of Wednesday, followed by Mississippi and Georgia.

Texas' governor has issued a mandate requiring face masks, and Mississippi temporarily mandated mask-wearing in public statewide this month. Georgia has not issued a statewide mask mandate.

As Georgia schools reopened this month, some reported hundreds of students and staff were in quarantine after officials identified positive cases. A photo of a crowded high school hallway with nearly no masks in sight raised concern across the country. One school district announced it would begin the year with virtual learning after more than 90 staff members were forced to quarantine.

An August 16 White House Coronavirus Task Force report obtained by The Atlanta Journal-Constitution recommended that Georgia do more to fight Covid-19 spread, including closing bars and gyms, limiting indoor dining at restaurants and reducing social gatherings to 10 or fewer people.

Gov. Brian Kemp pushed back Wednesday, a day after his state topped the rankings by population.

"If we're the highest (per) capita in the state right now, that's because Texas and Florida and Arizona and some of the states that were peaking a week or two ago are on the downclimb," Kemp told reporters.

Georgia's seven-day average of new daily cases was around 2,500 Wednesday -- down from a plateau of around 3,700 daily in late July, Johns Hopkins data show.

How schools are responding

Colleges in at least 15 states have reported Covid-19 cases on campus, with outbreaks traced to off-campus gatherings, athletics, Greek life, dorms or move-in testing.

The University of Mississippi said Wednesday that 15 student-athletes and one employee tested positive for the virus. Of the athletes, 11 are on the same team, but the university did not say which sports the positive tests came from.

At the University of Connecticut, several students were removed from their on-campus housing after the university found they held an "unapproved gathering in a residence hall room."

Fourteen Drake University students were asked to leave campus for two weeks after violating an agreement signed by students outlining safety protocols.

The University of Notre Dame said all undergraduate classes will be remote for the next two weeks as it tries to control a spike in cases. Michigan State University has announced the year will start remotely for undergraduate students. In New York, Ithaca College said remote instruction will be extended through the fall semester.

In Detroit, a union for K-12 teachers said Wednesday members voted in favor of a potential strike in a bid to change the school district's reopening plan. The district currently intends to start September 8 with some classes online and some in person; the union says the vast majority of teachers want to teach online for now.

Dr. Ali Khan, dean of the University of Nebraska Medical Center's college of public health, said Thursday that schools should reopen for in-person classes only when community transmission of Covid-19 is very low.

"Until then ... we'll do this sort of back and forth where they go to school, (then the schools) shut down" for a little bit, resume, and then close for the year, Khan told CNN's "New Day."

Wait a few weeks after exposure before testing for anitbodies, group says

People who want to know whether they have antibodies after being exposed to Covid-19 should wait a few weeks after exposure before getting an antibody test, experts said during a briefing Thursday.

A panel of the Infectious Diseases Society of America recommends "against using antibody testing in the first one or two weeks after exposure to infection, because many patients haven't developed antibodies yet," said panel chairwoman Dr. Kimberly Hanson.

The society reviewed several studies on antibody testing.

"Three to four weeks after the onset of symptoms -- this is the sweet spot, this is where the tests have the highest sensitivity and the highest specificity," Dr. Angela Caliendo said during the briefing.

Antibody tests are used to see whether a person was infected with Covid-19 in the past -- not to be confused with diagostic tests, which are meant to determine whether someone is infected now.