"We are in various stages of discussions with our landlords regarding ongoing rent obligations, including the potential deferral, abatement and/or restructuring of rent otherwise payable during the period of the COVID-19 related closure," Cheesecake Factory said in an SEC filing.

Notably, earlier this week, national restaurant chain The Cheesecake Factory said it will not be paying rent in April, as its shops remain shut to the public because of COVID-19. It has 294 locations across North America, many of which are in enclosed shopping malls. Cheesecake Factory also is furloughing roughly 41,000 hourly workers.

"The rental income that we receive from tenants is essential in order to meet these obligations," Taubman said. "All tenants will be expected to meet their lease obligations." (See the full memo below.)

In a memo dated March 25, which was obtained by CNBC, the real estate investment trust said it still has its own obligations to meet — such as paying lenders on mortgages and paying for utilities.

U.S. mall owner Taubman is telling its tenants that they must pay rent amid the coronavirus pandemic.

A view of the Cheesecake Factory at the Short Hills Mall on March 18, 2020 in Millburn, New Jersey.

Taubman has one Cheesecake Factory location, according to an analysis by RBC Capital Markets and Costar Realty. The biggest mall owner in the U.S., Simon Property Group, has 29 of them.

Real estate analysts tell CNBC that Cheesecake Factory's decision — to forego making rent payments — will likely set a precedent for other restaurant operators and retailers to follow suit. Many have been in talks, CNBC previously reported, over what to do about paying these bills. The consequences of still having to pay rent on a location that is not in business could deal a huge blow to some retailers that are already strained for cash.

But landlords, such as Taubman, are also still on the hook, even if their malls are entirely shut down for the time being. Many of them have properties backed by mortgages that must be paid on.

"I have no idea where this is going to shake out," Vince Tibone, a lead retail analyst at commercial real estate services firm Green Street Advisors, said in an interview. But landlords and tenants will end up "sharing the burden," in some way, he said.

Taubman announced earlier this month that all of its properties will be closed through at least the end of March, except for two centers, which are open-air. The announcement by Taubman came a day after its larger rival, Simon, said it was shutting all of its malls and outlet centers temporarily, to try to help halt the spread of COVID-19.

Simon in February said it would be acquiring Taubman, in a deal valued at $3.6 billion. The transaction is still expected to close in 2020.

"We are attempting to navigate through this situation in the best way we can, while being as flexible as we can with our tenants in light of our ongoing obligations," a Taubman spokeswoman told CNBC in an emailed statement on Sunday.

"The tenant memo does not replace our willingness to talk to each tenant about their respective challenges and help them chart an appropriate course for the future," she said. "In fact, we've had numerous calls with our long-standing tenants and most fully understand our position as it is a challenging time for all involved. Naturally, the environment is much harder for smaller, less-established temporary occupants that may only be operating in one center."

Here is the letter sent to Taubman's tenants, dated March 25, in full: