Simon Property Group, the operator of many top caliber U.S. malls, such as Roosevelt Field on Long Island, N.Y. and Stanford Mall in Palo Alto, Calif., is contending with many tenants like Gap, Cheesecake Factory, and Urban Outfitters declining to pay rent for April. Some are holding out for May, too, as stores have been largely closed across the country because of the COVID-19 outbreak.

But David Simon, the son of the company's co-founder, told Wall Street analysts on Monday night he expects tenants to honor their contracts, even as the companies have taken dramatic steps to preserve cash during mass store closings: furloughing staff, drawing down credit, and cutting dividends.

"We have a lease, and they have to pay," Simon said.

He declined to say how many tenants have declined to pay. Rival mall developer Macerich on Monday said it has so far collected 26% of rents billed for April and 18% for May. Brookfield was at 20% for April, suggesting collections have been paltry for Simon, too.

Still, Simon's shares rose 10% after the company said it would pay its dividend, that dozens of its more than 100 malls had already reopened as some states ease their lockdowns, and that by next week, half of its retail space would be open to the public. (Simon also operates several dozen outlet centers.)

For now though, Simon faces tough negotiations with many retailers grappling with the vaporization of sales in April and are anticipating a slow return when they do reopen stores. Last week, Macy's CEO Jeff Gennette told Fortune sales might be 20% of normal levels in their first week after reopening, coming back gradually. Gap Inc CEO Sonia Syngal wouldn't say if her company, which pays $115 million in monthly rent for its North American stores, had resumed paying in May, but did allow that she sees the opportunity to rethink (code for permanently close) the size of the Gap and Banana Republic fleets.

Either way, landlords won't escape retail's pain, and Simon should brace for more stores withholding rent payments.、

"It seems unrealistic to believe these tenants will be able to pay deferred rent," GreenStreet Advisors wrote in an analyst note. "Despite the aforementioned rhetoric, we continue to believe most rent not collected on time will turn into rent abatement, not deferral." What's more, the research firm warned, Simon and other developers should brace for a downward re-setting of rent rates.

Adding to the pain: the closing of many anchor department stores. Macy's was already planning to close 125 stores, and the COVID-19 crisis could lead it to close more. Last week, Nordstrom said it was closing 16 of its full line department stores, the first large-scale closure program in its history, and Neiman Marcus filed for Chapter 11 bankruptcy protection, raising the likelihood it will close at least a few stores. J.C. Penney, which has 800 stores, is reportedly looking into seeking Chapter 11 protection too.

Anchor tenants disappearing is painful for mall owners in two ways. They generate a ton of shopper traffic for the mall as a whole, which is why they typically pay a very modest rent. But more worryingly for Simon and its peers, the disappearance of anchors can set off so-called co-tenancy clauses that can allow some tenants to break their lease. Such clauses call for a certain percentage of space in a mall to be occupied or for there to be an anchor tenant, typically a department store or a grocer.

For now, Simon prefers to focus on some green shoots. "For the retailers that are opening, they're gaining market share. They're taking advantage of pent-up demand," Simon said, noting that sales have been better than expected. But with the majority of retailers still dark and many opting for measures that limit store visits, business won't pick up all that quickly.

Simon suggested that was beside the point. The pressing need, he said, is to get people back in the habit of going to stores, even if the ramp up is gradual, and to see what safety measures work as more centers reopen.

"[Shoppers] want to see more stores open, as do we, but I think it's a process, and you got to get started and you go from there," said Simon.