JUDY WOODRUFF: But, first: how the Muslim community in Orlando is responding to the mass shooting.

As investigators continue to try to understand the motives of the Orlando shooter, the fact that he was a Muslim has put another community of American Muslims in an uncomfortable spot, disavowing the actions of an extremist, while also facing a backlash themselves.

William Brangham has the story.

WILLIAM BRANGHAM: As news broke early Sunday about the killings in Orlando, Joshua Weil thought what many Muslims thought about the attacker.

JOSHUA WEIL, Islamic Center of Orlando: My first thought is always, and sadly, like, please don't let him be Muslim.

WILLIAM BRANGHAM: Weil is a member of the Islamic Center of Orlando, one of the largest Muslim mosques in this area. Of course, news quickly broke that the killer, Omar Mateen, was, in fact, a Muslim. The attacks occurred right after Saturday night's Ramadan prayers.

JOSHUA WEIL: The thought occurred to me that, if this guy was Muslim, he probably just left one of these mosques. He might even have left this mosque. He might've been standing and praying Taraweeh, like, standing side-by-side with his brothers and listening to the Koran, and then he left that to go murder all these people.

WILLIAM BRANGHAM: Tariq Rasheed is the imam of this mosque.

IMAM TARIQ RASHEED, Islamic Center of Orlando: Every Muslim in this country and in Orlando is grieved. And they are in shock. They are asking questions, how can this happen here in Orlando? How can a person with Muslim faith can do this?

So, you know, people are very much in a shock, I can tell you, everyone. And then — and there is a fear factor as well, that you know there might be a backlash.

WILLIAM BRANGHAM: The mosque held a candlelight vigil for the shooting victims the night after the killings, and they have publicly and repeatedly condemned the attack, saying Mateen's actions are no reflection of their religion.

Imam Rasheed says this is the new reality for the American-Muslim community, having to account for the violent actions of a few extremists who claim to share their faith.

IMAM TARIQ RASHEED: We have nothing to do with this. We don't know who this guy was, where is he coming from, because terrorism has no religion. And, in religion, there is no terrorism.

WILLIAM BRANGHAM: This is what happened in San Bernardino and what happened at the military base in Texas, where one of these events occur and then the Muslim community is called to condemn. Are you guys sick of being asked to condemn?

SYED QUADRI, Orlando Resident: Absolutely. Sick is the right word. We are sick of this.

WILLIAM BRANGHAM: Syed Quadri and his wife, Rabana Khan, and their three kids are members of this mosque. Syed's a psychiatrist and Rabana is an accountant who helps manage his practice.

RUBANA KHAN, Orlando Resident: I actually was terrified and finding out what exactly happened. And of course, our heart goes out to all the mothers and fathers who have lost their kids. It's unfortunate. And it's terrible that these kinds of incidents are continuing to happen. And it's putting a bad name on the Muslim community.

WILLIAM BRANGHAM: Many people believe there is something about Islam that draws a paranoid, radicalized thinking. What do you say to people who think that that part — that that's part and parcel of your faith?

SYED QUADRI: Well, I'm not going to deny that. There is radicalism in every religion, I think, you know? Islam gets attention because of everything that's going around in the world. And I'm not going to say these people are not radical Islamists. Definitely, they are, but they are not a part of Islam.

We do not consider them Muslims. We do not consider them a part of Islam. Islam is all about peace, nothing to do with hatred or violence.

WILLIAM BRANGHAM: But these repeated disavowals haven't stopped the threats. The mosque's Facebook page, beneath its tributes to the victims, has been repeatedly covered with death threats and angry denunciations of Islam. The mosque says they have received similar voice-mail messages.

Joshua Weil says most of these are likely just angry venting after the attacks, but some of them were simply too specific to ignore.

JOSHUA WEIL: He see us parasites at the Publix at Hialeah all the time.

WILLIAM BRANGHAM: The grocery store.

JOSHUA WEIL: Yes. The grocery store on Hialeah all the time, and that the next time he sees one of us, he's going to take care of them.

And that was the one that got us most. We contacted the police with that one.

WILLIAM BRANGHAM: The mosque alerted the police, but now they have also hired an armed guard to patrol the grounds during prayer services.

Imam Rasheed says Ramadan is usually the busiest time at the mosque, but now people are afraid to come.

IMAM TARIQ RASHEED: Sisters in the community, they texted me, you know what, I'm not coming today. You know, we are fearful. We don't want to come. And they didn't send their children.

You know, we have never done this. We have never done this. And this mosque has been in operation for the last 32 years.

WILLIAM BRANGHAM: Weil says that he and his wife, Anna, who's also Muslim, don't want to give into fear, but he understands it. Weil is a teacher by day, and also works as an outreach director for the mosque.

He says, especially at times like this, people need to worship together, not apart. But Anna said, she thinks the anger out there is serious enough to stay away from the mosque for now.

ANNA WEIL, Orlando Resident: We have not gone to the mosque for dinner, for prayers or anything since the shooting happened.

WILLIAM BRANGHAM: You and the kids?

ANNA WEIL: Yes.

WILLIAM BRANGHAM: Weil says these attacks have also shined a light on a generational divide within the Muslim community over the issue of homosexuality.

He says most of the younger American-born Muslims here have condemned the attacks and embraced the gay community that's been victimized by this killer. But he says some of the older generation, those largely born abroad in much more conservative societies, have struggled with how to respond.

JOSHUA WEIL: They want to condemn this. They want to — they do believe it's horrible and they do think that it never should've happened, but they don't want to go as far as to, you know, embrace or say that they support homosexuality, and they kind of feel that this awkward place. It's almost been nice to see some of them reluctantly move in and say, no, we see now this is a community that we should be supporting.

This is a community that faces all of the same bigotry and all of the same, you know, anger and aggression from many of the same people that we do.

WILLIAM BRANGHAM: The reverberations from this attack have also spilled onto the campaign trail. Citing Orlando, Donald Trump doubled down on his call to ban Muslim immigration, although the shooter was born in New York City.

President Obama and some GOP leaders have again condemned that proposal.

What is your response when you hear some of the political rhetoric that happens — that flows after attacks like this?

SYED QUADRI: It is unfortunate that some people take advantage of these kinds of incidents. And, you know, they are banking on their votes. They are trying to build their political careers out of all those. That's all I can say.

RUBANA KHAN: Well, I consider myself an American and an American Muslim.

SYED QUADRI: Absolutely.

RUBANA KHAN: So, and I — it hurts that if somebody would try to take that away from me, because this is my country. This is where I grew up. So, when you tell me to leave, where am I supposed to go? You give me an answer.

SYED QUADRI: That's right. That's right.

RUBANA KHAN: This is my home.

WILLIAM BRANGHAM: The Muslim community here hopes the anger directed at them will soon subside and that the whole Orlando community can continue its slow process of healing from this tragedy.

For the "PBS NewsHour," I'm William Brangham in Orlando, Florida.