Forty nine people were killed in the incident at Pulse, a gay nightclub, and another 53 were injured, authorities said. It was not immediately clear whether the toll included the gunman, identified as Omar Mateen, 29, from Fort Pierce, Fla.

On social media, some noted a grim irony: Although Mateen had chosen a gay club as his target, it is still very difficult for gay men to donate blood in the United States.

Shortly after OneBlood's call went out, a rumor began circulating online that the tragedy had resulted in what was being characterized as a small but important victory for gay rights. They said that OneBlood, going against Food and Drug Administration guidelines, was willing to accept donations from anyone — including men who have recently had sex with other men.

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That claim turned out to be false. Pat Michaels, a spokesman for the blood bank organization, said in a phone interview that OneBlood is continuing to adhere to the longstanding federal restriction on sexually active gay men from donating blood. Although the FDA recently updated its guidelines to allow men who have not had sex with another man within a year’s time to donate blood, Michaels said OneBlood’s system has not yet been updated to allow that, but it will happen later this year.

The controversy has triggered much debate about how federal rules that prevent many gay men from giving blood are discriminatory.

At the end of last year, the FDA lifted a categorical ban on blood donation by men who have ever had sex with another man. Yet men who have had sex with a man in the past year are still barred from giving blood.

The agency said that the 12-month ban is supported by scientific evidence, that it is consistent with international practices and that it will help prevent the spread of HIV.

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Data from the Centers for Disease Control and Prevention show that Florida is the state with the second-highest rate of HIV-positive diagnoses, after Louisiana. There were more than 31 positive diagnoses for every 100,000 adults in Florida as of 2014.

Opponents of the rule argue that the waiting period should be no more than 30 days, given the fact that testing can detect the virus soon after infection.

"The one-year deferral policy is still rooted in an outdated, insulting vision of gay men as diseased, promiscuous lechers," wrote Mark Joseph Stern in Slate. "A gay man in a decades-long monogamous relationship with his husband will be forbidden from donating blood."

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Researchers at the University of California at Los Angeles have estimated that allowing gay men to donate blood could add as much as 615,000 pints a year to the national supply — an increase of 2 percent to 4 percent.

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On Sunday, OneBlood was able to start refilling its bank with donations despite the restrictions. Volunteer donors have posted pictures on social media of lines with hundreds of people at numerous OneBlood locations throughout the country, and the organization said it is extending hours at many of those centers.

Michaels said the response so far has been “overwhelming, especially here in central Florida.”

He said that while OneBlood is urging people with O-negative, O-positive and AB plasma blood to donate immediately, the organization is asking people with other types of blood to “please hold on until we can assess what else we need.”

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“We have hundreds of people showing up to our locations,” he said. “We understand the sentiment that people want to help and that giving blood is a profound way to help, but we are asking those who have other blood types to give us some space for now.”

This post has been updated.