A 46-year-old man has been charged after 11 people died in a shooting at a synagogue in the north-east US city of Pittsburgh on Saturday, officials said.

Robert Bowers faces 29 counts including 11 of murder and 11 of obstructing the exercise of religious beliefs resulting in death, the US Attorney's Office for the Western District of Pennsylvania said.

Another six people were injured, including four police officers who went to tackle the gunman after he stormed into the Tree of Life synagogue during a baptism on Saturday morning and opened fire.

"It's a very horrific crime scene," Wendell Hissrich, the city's public safety director told reporters earlier Saturday. "It's one of the worst that I've seen and I've been on some plane crashes."

After killing the 11 victims, the suspect was engaged by local police before retreating back into the synagogue, Bob Jones, the FBI official responsible for the investigation, told reporters.

He was carrying an assault rifle and three handguns during the attack, according to Jones. They were apparently purchased legally.

Bowers himself was also shot and was being treated in hospital. No children were among the victims.

Scott Brady, US attorney for the Western District of Pennsylvania, praised police for their bravery, saying they had run towards the gunfire. Justice would be "swift" and "severe," he added.

US Attorney General Jeff Sessions said the charges would include some that could lead to the death penalty.

Jonathan Greenblatt, head of the Anti-Defamation League, which campaigns against anti-Semitism, said that it was "likely the deadliest attack on the Jewish community in the history of the United States."

Emergency services were called to the synagogue at about 10 am (1400 GMT) after Bowers opened fire, reportedly shouting "all Jews must die." His social media profiles showed he was a weapons enthusiast with a history of anti-Semitism, US media reported.

The synagogue is located in Squirrel Hill, a Pittsburgh neighbourhood with a large Jewish population.

Between 50 and 60 worshippers would be there on an average Saturday morning, Jeff Finkelstein, a spokesman of the Jewish community in Pittsburgh, said at the scene.

Finkelstein said around 50 per cent of Pittsburgh's Jews lived in Squirrel Hill, where a multi-faith vigil was held later Saturday.

US President Donald Trump condemned the shooting as an "evil Anti-Semitic attack" and "an assault on humanity" on Twitter, and later ordered all flags to be flown at half-mast on public buildings.

In the past he has been criticized for failing to adequately condemn hate crimes, for example after the death of a woman at a white supremacist rally in Charlottesville in August, 2017.

Earlier Saturday he responded by pushing for more armed protection to prevent shootings, saying an armed guard on site would have made the outcome "far better."

"If they had some kind of a protection inside the temple, maybe it could have been a much different situation," said Trump, who has advocated arming guards and other officials at schools and other public sites.

By contrast, the state's governor responded with a condemnation of US gun policy.

"We have been saying 'this one is too many' for far too long. Dangerous weapons are putting our citizens in harm’s way," Pennsylvania Governor Tom Wolf, a Democrat, said at the scene.

The shooting comes days after a far-right attack in which packages containing pipe bombs were sent to several Trump critics and prominent left-wing figures.

Police later arrested a man, revealed to be a Trump supporter, in Florida after packages were sent to high-profile Democrats including former president Barack Obama, former secretary of state Hillary Clinton and former vice president Joe Biden.

After Saturday's attack, Israeli Prime Minister Benjamin Netanyahu condemned what he called "horrendous anti-Semitic brutality," adding that the "entire people of Israel grieve with the families of the dead."

Diaspora Minister Naftali Bennett meanwhile said he would fly to Pittsburgh to visit the scene of the attack, meet the local community and attend the funerals of the victims.

Other countries around the world also expressed their shock at the shooting.

German Chancellor Angela Merkel expressed her condolences to the families of the dead, who she said were "apparently victims of blind anti-Semitic hatred," according to her spokesman Steffen Seibert.

French Interior Minister Christophe Castaner meanwhile said he had ordered security at synagogues around France to be increased over the weekend.