The Florida department of health has levied a $3.5m fine against a county government for requiring its employees to provide proof of a Covid-19 vaccination.

The state is also investigating other government entities, schools and businesses, including a Harry Styles concert, for violating its ban on asking people to provide proof of vaccination. The ban went into effect last month and Texas put a similar ban in place on Monday.

Florida fined Leon county $5,000 for each of the 714 employees it asked to provide proof of vaccination by 1 October. The health department said 700 employees met this requirement and the 14 employees who did not were terminated several days later.

Florida’s governor, Ron DeSantis, said the state health department would continue to enforce the ban. “We’re going to stand up for Floridians’ jobs, stand up for Floridians’ livelihoods, and stand up for freedom,” DeSantis said in a statement.

The Florida and Texas bans challenge Joe Biden’s planned rule for companies with more than 100 workers to require proof of vaccination or weekly testing. Biden announced the rule in September but its details are still being worked out.

At a White House press briefing on Tuesday, the press secretary, Jen Psaki, said the administration stands by vaccine requirements, including in states that oppose them.

“I think it’s pretty clear when you make a choice that’s against all public health information and data out there that it’s not based on what is in the interest of the people you are governing,” Psaki said. “It’s perhaps in the interest of your own politics.”

Several recent polls have shown a majority of Americans support workplace Covid-19 vaccine requirements. About 60% of Americans support vaccine mandates for federal workers and employees of large companies, according to a poll published by Gallup in late September.

Florida’s health department is investigating more than 100 businesses and government agencies for violating its ban, according to a list obtained by the Orlando Sentinel newspaper. Businesses in potential violation of the ban include a Harry Styles concert, Disney Cruise Lines and a state counter-terrorism squad.

The Leon county administrator, Vincent S Long, said in a statement that the county would use “any remedies available” to settle its dispute with the state.

Long said: “The county strongly contends that our employee vaccination requirement was not only completely legally justifiable, but it was a necessary and responsible action to take to keep our employees safe, protect the public, and ensure our readiness as a frontline response organization.”