As visitors to supermarkets across the Houston area see empty shelves amid increased demand prompted by the coronavirus outbreak, grocery executives on Monday assured the public that they will continue to meet that demand.

Representatives from H-E-B, Kroger and Randalls joined Mayor Sylvester Turner to quell rumors that the stores would close or run out of food, making it clear that “there is no issue with the food supply chain,” a message that was repeated like a mantra as concerns grew over panic buying and grocery stockpiling.

“No need to rush into the stores, as if all of the food will be gone, and there won’t be any left to restock,” Turner said. “No, no problem with the food supply chain, and they will be able to restock the shelves.”

While none of the stores are shutting down, according to store representatives, all major chains have cut store hours across the region.

H-E-B and its affiliated stores — Joe V’s, Mi Tienda, and Central Market — are open from 8 a.m. to 8 p.m. until further notice. All Kroger stores are now open from at 7 a.m. to 10 p.m. Randalls will now be open from 7 a.m. to 9 p.m. And Fiesta will open from 9 a.m. to 8 p.m.

But despite the increased demand, all the stores say they are still getting full shipments, and have worked with the city’s Office of Emergency Management to prepare for similar situations.

“The real challenge is getting it to the shelf,” said Joe Kelley, president of Kroger’s Houston division.

Each store is taking its own steps as the virus, which has already been confirmed in about 30 people across the greater Houston area, spreads. And each store said to meet demand they are hiring new people.

Kroger is limiting the number of people in its stores at one time, and is working with distributors to prioritize necessities like water, and baby and sanitation products, Kelley said. The store will also donate $3 million to hunger relief groups Feeding America and No Kid Hungry, he added. Randalls was working on new schedules for suppliers and manufacturers, according to  Christy Lara, a spokeswoman for Randalls.

H-E-B president Scott McClelland said the chain is enacting a number of new measures to protect customers and staff, including sneeze guards to separate cashiers and customers, and a staggered entry system, to limit the distance between customers. There is also hand sanitizer and cart sanitizer at each location.

He also asked people not to visit the stores if they’re feeling sick.

McClelland, addressing reports of curbside orders being cancelled, said capacity was a problem. But he said the chain was already working on ways to free up employees to work in the most-essential areas, including eliminating floral departments.

“We’ve been through this before, with the hurricanes,” McLelland said. “And it really brings out the best in Houston, because we all come together. Although, this one is different, because in a hurricane lots of people leave town. Here everyone is staying. And most people are staying home to eat.”

Even if shelves seem bare one day, there will be more coming, McClelland added.

“There will be food,” he added later. “There’s not a reason to stock up. Just come back tomorrow.”