WASHINGTON, Oct 14 (Reuters) - President Joe Biden touted the success of mandates in spurring vaccination against COVID-19 in the United States on Thursday but said more needed to be done to get the 66 million people who are eligible but still unvaccinated to get the shot.

Vaccination rates against COVID-19 in the United States have risen by more than 20 percentage points after multiple institutions adopted vaccine requirements in recent months, while case numbers and deaths from the virus are down, Biden administration officials said on Wednesday.

Biden said in July federal workers needed to be vaccinated or get tested regularly. In September, he said federal workers needed to be vaccinated or face losing their jobs, and that employees at big companies needed to get jabs or be tested.

"The vaccine requirements that we started rolling out in the summer are working," Biden said, noting that the Labor Department's completed rule on vaccination requirements for businesses would be coming out shortly.

"We’re down to 66 million, still an unacceptably high number, of unvaccinated people," he said. "We can't let up now."

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The latest Reuters update shows 66.3% of the United States population has received at least one shot and 57.3% are fully vaccinated. Administration officials said Wednesday 77% of eligible Americans had received at least one shot.

Some Republicans have pushed back on the mandates, including Texas Governor Gregg Abbott, who issued an executive order banning companies from mandating vaccines in the state. Some companies that operate there say they plan to ignore the ban.

"Vaccination requirements should not be another issue that divides us," Biden said.

Vaccines for children ages five to 11 are expected to be approved in the United States by year-end. Biden said a decision on that authorization by the appropriate authorities was expected in the next few weeks.

"If authorized, we are ready," Biden said, adding the government had purchased enough vaccines for those children.

(Reporting by Steve Holland and Jeff Mason; Editing by Heather Timmons and Mark Heinrich and Kirsten Donovan)