Fauci's comments to ABC's "Good Morning America" echoed fellow White House coronavirus task force member Dr. Deborah Birx, who recently visited those states to warn their numbers were headed the wrong way.
Test positivity rates there have been rising, Fauci said. Tennessee on Monday saw its highest seven-day average of new daily cases, at well over 2,000.
Tennessee's average was around 750 per day a month ago, according to data from Johns Hopkins University.
"We just can't afford, yet again, another surge" like that seen in recent weeks in Florida, Texas, Arizona and California, Fauci told ABC.
Wearing masks, social distancing, closing bars where virus spread is high, and washing hands can help turn the tide, he said. He also repeated what he'd recommended in April: Reopen economies in phases, crossing each phase only after seeing cases decrease over 14 days. States largely ignored that advice.
"We would hope that (states) all now rethink at what happens when you don't adhere to that," Fauci told "Good Morning America."
Health officials are urging states to implement stricter measures after weeks of surges in new cases following reopenings that mostly began in May.
Across the US, at least 27 states have paused or rolled back their reopening plans and imposed new restrictions. More than 40 states have some kind of mask requirement.
The efforts may be helping:
• In Arizona, Texas and Florida, which have seen rapid case spread since June, new cases have flattened or slightly decreased recently.
• Monday's nationwide new case total of 56,336 was the second-lowest in the past 20 days.
• The country's seven-day average for new cases was 65,083 on Monday, the lowest figure since July 15.
However, deaths and hospitalizations from coronavirus are creeping higher. The seven-day average for daily deaths Monday was 998, the highest since June 2. And the number of daily hospitalizations has been over 57,000 for nearly two weeks, hovering close to the April peak of 59,940.
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States crack down on social gatherings
Birx has said that among the states officials are tracking, there seems to be a "household" pattern of infections that starts with young people, usually less than 30 years old. Those residents, who are usually asymptomatic, then transmit the virus to their parents who then transmit it to other, older residents, she said.
In Mississippi, about 80% of surveyed coronavirus patients said they had attended a social gathering, including funerals and birthday parties, where people weren't adhering to social distancing. And in New Jersey, health officials said they have seen multiple outbreaks arising from gatherings of young people.
To stem those infections, states have cracked down on settings where people congregate -- like bars -- and pleaded with younger groups to heed guidelines including wearing masks and social distancing.
In Columbus, Ohio, the city council approved
