The gunman who opened fire on a Pittsburgh synagogue on Saturday morning (local time), killing 11 and injuring six more, has been named as 46-year-old Robert Bowers, a Trump-hating antisemite who regularly complained on social media about the president and "the infestation" of Jews.

Bowers, who professed his disdain for President Trump on social media as he spewed vile antisemitism an hour before Saturday's attack, opened fire at the Tree of Life Congregation Synagogue in the Squirrel Hill area of Pittsburgh shortly before 10am.

Less than an hour after posting the threat: "I'm going in" on the social media site Gab.

He was enraged by HIAS, the Hebrew Immigration Aid Society which helps Jewish migrants settle in the US, which he accused of bringing 'invaders in that kill our people'.

"I can't sit by and watch my people get slaughtered. Screw your optics, I'm going in," he wrote.

Law enforcement officers secure the scene where multiple people were shot. Photo / AP

Two days ago, he said there was no "MAGA as there is a k*** [ethnic slur for a Jewish person] infestation."

A photograph at the top of Bowers' profile showed a machine with the numbers 1488 - a prolific white supremacist symbol - on it.

He also previously wrote that he had never voted for Donald Trump, "nor have I owned, worn or even touched a maga hat".

Shortly before 10am, he burst through the synagogue's doors and opened fire on a Shabbat service congregation on the main floor where around 40 to 50 people had gathered, shouting "all Jews must die!".

After killing three people on the main floor, he went downstairs, where the New Light congregation was gathering in the basement, and opened fire there.

He murdered four people there then fled upstairs where, on the third floor, he exchanged fire with SWAT teams and injured four police officers. Dor Hadash, a third, smaller group, was gathered in the rabbi's study to the side of the Tree of Life' s congregation.

After being injured himself in the crossfire, Bowers surrendered to police. He is now in custody.

Among the six people injured were four police officers and two congregants who are clinging to life in the hospital.

None of the 11 people killed have been named. Local officials described the scene as "horrific" and cried as they gave an update on the shooting on Saturday afternoon.

After tweeting that the situation was "devastating", President Trump said on Saturday that it would not have happened if the synagogue had had its own security.

He called for the shooter to be sentenced to death and spoke about making capital punishment "in vogue".

People hug outside the Tree of Life Congregation after multiple people were shot. Photo / AP

The horror began unfolding on Saturday shortly after the 9.45am services began. In addition to the Sabbath service, a bris was scheduled for the morning and had attracted additional worshipers.

Bowers started his killing in the main chapel where the Tree of Life congregants were gathered. He shot indiscriminately, according to survivors, then made his way down to the basement where one of the other two groups was.

After killing seven people between those two floors, he made his way to the third floor.

By then, SWAT teams had arrived at the scene. They engaged in a gunfight with him and four cops were shot in the process. None are thought to have suffered life threatening injuries

Bowers was injured in the battle and surrendered to police by crawling to them. He was taken to the hospital.

Speaking afterwards, Wendell Hissnich, Pittsburgh Director of Public Safety, fought back tears as he described the scene inside.

"It's a very horrific crime scene. It's one of the worst that I have seen and I have been on plane crashes. It is very bad," he said.

One woman, whose daughter was inside at the time, told CNN: "They heard the shots and they all, her friend's mom and dad and son, they just all ran downstairs I guess and barricaded themselves in the basement.

"They kept hearing gunfire and everything else."

Another man rushed to the scene to try to get his elderly father-in-law to safety. He told reporters: "My father-in-law was inside, I got married in this place, this is crazy.

"This is unbelievable. People have to stop the hate. They have to stop."

President Trump spoke about the atrocity as he boarded Air Force One at Joint Base Andrews. He asked why the synagogue did not have its own security and suggested that fewer would have died had an armed guard been stationed there.

"If there was an armed guard inside the temple that would have been able to stop him, maybe there would have been nobody killed except from him.

"We can look at it two ways. But if they had somebody to protect people... isn't it a shame that we even have to speak that way?

"That we even have to think that way inside a temple... but certainly the results should have been better," he said.

Asked if he thinks every place of worship should have armed security, Trump replied: "I hate to think of it that way.

Police respond to an active shooter situation at the Tree of Life synagogue. Photo / AP

"It's certainly an option. This world, this is a world with a lot of problems and it has been for many years, many many years, and you could say for many centuries but certainly you want protection and they didn't have protection.

"They had a maniac walk in and the didn't have any protection and it's so sad to see. So sad to see.

"It's a very difficult thing for me to stand as president and watch.

"Before I ran for office, I watched instances like this and I'd say, 'what a shame, what a shame.' It's tougher when you're the president of the United States and you have to watch this kind of thing happen. It's so sad to see."

He praised the "outstanding" law enforcement and said the gunman was able to get access when he shouldn't have been because of the lack of security.

"You look at the violence all over the world. It comes back in the form of a mad man, a wacko. We should stiffen up our laws in terms of the death penalty, they shouldn't have to wait years and years.

"I think they should stiffen up laws and bring the death penalty in to vogue," he said.

Vice President Mike Pence later said: "What happened in Pittsburgh today was not just criminal, it was evil.

"An attack on innocent Americans and an assault on our freedom of religion.

"There is no place in America for violence or antisemitism and this evil must end."

There was no security at the Tree of Life on Saturday, with former synagogue leaders describing how it operates an open-door policy for worshipers and only puts security on for significant holidays despite fears among community leaders that such a shooting was on the horizon.

"On a day today the door is open you can walk in an out. Like most religious institutions, we have an open door," the synagogue's former president, Michael Eisenberg, told CBS Pittsburgh.

He added that security had been a "major" concern for him in the past and that he was working with the government to improve escape routes and emergency procedures.

President Donald Trump speaks to reporters about a shooting at a Pittsburgh synagogue as he arrives at Air Force One. Photo / AP

"It was a major concern for me, for us.

"We were working with the DHS to evaluate exit routes, I just spoke to our maintenance person who was able to get out.

"We were working with the other synagogues on what to do if this happened," he said.

He said of the building's maintenance man, who witnessed Saturday's shooting and escaped through one of the exit doors,: "He was shaken, he saw one of our congregants down, he knew, he was in the bathroom and he was able to get out of the building."

A former rabbi said he was grateful that many of the congregants often arrived late for morning services and that he was grateful on this occasion.

"I thought about it all the time I have to tell you when I was there I always had the thought in the back of my had unfortunately in the world we live in," the former rabbi said.

The area was put on lock down, with any residents living nearby told to lock their doors and not go outside. Witnesses are still being interviewed by police at the scene.

He was "crawling" and injured before he was arrested.

President Trump tweeted first that he was aware of the unfolding scenario, writing: "Watching the events unfolding in Pittsburgh, Pennsylvania.

"Law enforcement on the scene.

"People in Squirrel Hill area should remain sheltered. Looks like multiple fatalities. Beware of active shooter. God Bless All!"