The World Health Organization recommended that certain hospitalized Covid-19 patients be given a type of anti-inflammatory drug found to reduce the risk of death by 13% in the sickest patients when taken in combination with steroids.

The global public-health agency updated its Covid-19 treatment guidelines on Tuesday to strongly recommend that people with severe or critical disease be given drugs tocilizumab and sarilumab to combat the haywire inflammatory immune reaction of some patients.

The drugs are designed to block a protein called interleukin-6, or IL-6, that is thought to play a role in the hyper-inflammation experienced by some Covid-19 patients.

The WHO said the drugs are the first found to be effective against Covid-19 since the agency recommended the use of steroids in September.

“Patients severely or critically ill with Covid-19 often suffer from an overreaction of the immune system, which can be very harmful to the patient’s health,” the WHO said in a statement. “Interleukin-6 blocking drugs—tocilizumab and sarilumab—act to suppress this overreaction.”

The WHO said patients should be given either tocilizumab, sold under the brand-name Actemra by Roche Holding AG’s Genentech unit, or Sanofi SA and Regeneron Pharmaceuticals Inc.’s sarilumab, which has the brand name Kevzara.

Still, the WHO raised concerns about the price and availability of the drugs in low- and middle-income countries. The agency called on the drugs’ manufacturers to reduce prices and increase supplies, especially in countries where infections are surging.

“IL-6 receptor blockers remain inaccessible and unaffordable for the majority of the world,” WHO Director-General Tedros Adhanom Ghebreyesus said.

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The list price of Actemra is about $2,300 per dose, a Genentech spokeswoman said. The company already markets an intravenous form of the drug that can be used to treat hospitalized Covid-19 patients.

A Sanofi spokeswoman said Kevzara’s U.S. list price is about $1,830 a dose. The company doesn’t currently market a form of the drug that can be given with an IV.

Researchers began studying IL-6 drugs early in the pandemic but a number of large studies failed to show the drugs worked or produced inconclusive results.

Positive data from trials conducted by U.K. researchers in recent months, however, has helped rekindle interest and led regulators to reconsider authorizing their use.

The U.S. Food and Drug Administration last month cleared Roche’s Actemra for emergency use in certain hospitalized patients when used in combination with steroids.

Sanofi and Regeneron don’t plan to seek FDA authorization for Kevzara in severe or critically ill Covid-19 patients because their studies didn’t show a statistically significant benefit, the Sanofi spokeswoman said. The companies previously said they didn’t anticipate conducting further studies of Kevzara for Covid-19.

Sanofi is in discussion with the WHO and national health authorities about how to best support patients who might benefit from IL-6 blockers, the spokeswoman said. However, the spokeswoman noted that Kevzara isn’t authorized for Covid-19 by any health authorities. Because of Kevzara’s lengthy and complex manufacturing process, Sanofi’s priority is to maintain continuous supplies for patients taking the drug for its approved purpose of treating rheumatoid arthritis, the spokeswoman said.

The WHO’s revised treatment recommendations coincided with new research into the drugs’ effectiveness.

The WHO said its researchers found, in a review of 27 clinical trials including more than 10,000 patients, that the drugs reduced the odds of death by 13% compared with standard care alone in severely-ill or critical patients.

The data were published on Tuesday in the Journal of the American Medical Association.

Across all patients studied, the risk of death was 21% for patients who received the IL-6 blockers in combination with steroids, compared with an assumed 25% death among those who received usual care or placebo, the researchers said.

Two University of California, San Francisco, researchers—Michael Matthay, a doctor treating respiratory-failure patients, and infectious-disease specialist Annie Luetkemeyer—said in an editorial accompanying the study that IL-6 drugs hold promise for hospitalized patients with worsening disease who require substantial oxygen assistance “but are not yet merited for widespread use among patients with mild disease nor with prolonged invasive mechanical ventilation.”

Write to Joseph Walker at joseph.walker@wsj.com