San Francisco will pay for five additional sick days for private-sector workers harmed by the new coronavirus as it expands relief efforts. Mayor London Breed is setting aside $10 million to help those financially strapped by the growing pandemic.

The Workers and Families First Program, if fully used, would support over 16,000 additional weeks of sick leave pay, providing coverage for up to 25,000 San Francisco employees. In a statement announcing the aid package, Breed said the initiative will cover employees of San Francisco companies who are sick, caring for an ill family member or child whose school is closed, or affected by shelter-in-place orders, which began Tuesday in six Bay Area counties.

“Public health comes first in this crisis, but we know that many people have less flexibility to stay home and keep paying their rent if they do get sick,” Breed said in a statement. “We want everyone to know that staying home to take care of themselves and their families is the most important thing they can do, not only for their own health but also to slow the spread of this virus in our community.”

Officials said that all San Francisco businesses are eligible for the funding, and that 20% is earmarked for small businesses with 50 or fewer employees. The public funding will foot the bill for up to 40 hours per employee at $15.59 per hour, or $623. If the employee earns above minimum wage, the employer is responsible for paying the remaining costs.

Employees are eligible only if they have already exhausted their currently available sick leave or are ineligible for federal supplemental sick leave and if their employers agree to the extension. The city requires all employers to provide sick leave time equal to one hour for each 30 hours worked. Businesses with 10 or more employers may cap each worker’s sick time balance to 72 hours, and those with fewer than 10 can cap each sick time balance to 40 hours.

Breed also announced a policy permitting public workers to advance their paid time off in the event that they cannot work because of COVID-19 or related public health recommendations.

San Francisco’s policy would supplement the coronavirus aid package that the House passed Friday, which included sick pay for some workers, free testing and family leave.

The city also established a business relief fund last week with a $1.5 million donation from Salesforce, in addition to a separate fund with $1 million in city grants.

The San Francisco Chamber of Commerce is requesting that the city transfer unused money from HealthySF, the city’s employer-supported health care program, to help pay restaurant, bar and retail workers. It isn’t clear how much money is unspent, but it would be only a fraction of each restaurant’s payroll. The chamber said one restaurant, for example, paid $60,000 last year for the program, and has a $100,000 two-week payroll.

City assistance is welcome, but it’s only a minor lift to restaurants and bars facing an increasingly bleak situation, said Thad Vogler, owner of several San Francisco restaurants and taverns, including Bar Agricole and Trou Normand. Those businesses both closed temporarily last Friday, and on Monday, six Bay Area counties told residents to stay inside and ordered all nonessential businesses to close until at least April 7. Restaurants can provide delivery and takeout only.

“It doesn’t seem like it will make that much a difference,” Vogler said of expanded sick leave. “We just have no cash. It’s just a brutal state of affairs.” Vogler said his restaurants wouldn’t be able to compete in the delivery sector and will stay shuttered for now. The businesses are taking out a loan to pay workers for two weeks.

He hopes that landlords, vendors and employees will give him some flexibility that could include delaying payments. If so, Vogler expects that his businesses could survive a couple of months while staying shut.

Even after the coronavirus epidemic ends, Vogler expects many restaurateurs to reconsider if staying in the industry is worth it. Even when the economy was booming, businesses were struggling with low margins and high operating costs.

“You’re leaking, and then you get hit by a torpedo,” he said.

Megan Cassidy and Roland Li are San Francisco Chronicle staff writers. Email: megan.cassidy@sfchronicle.com, roland.li@sfchronicle.com Twitter: @meganrcassidy @rolandlisf