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A gunman faces 29 charges of violent crimes after opening fire during a baby-naming ceremony at a Pittsburgh synagogue on Saturday, killing 11 people and injuring six in the deadliest anti-Semitic attack in recent US history.

The shooter - identified as a 46-year-old Robert Bowers - reportedly yelled "all Jews must die" as he burst into the Tree of Life synagogue, where congregants gathered for Sabbath services.

Taken into custody after a shootout with police, the suspect was transferred to a hospital.

US prosecutors subsequently charged him with 29 counts of federal crimes, including 11 counts of using a firearm to commit murder and 11 counts of obstructing the exercise of religion resulting in death.

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"The crimes of violence are based upon the federal civil rights laws prohibiting hate crimes," a statement said. Authorities have said Bowers' charges could carry the death penalty.

US President Donald Trump denounced "a wicked act of mass murder," while his daughter Ivanka, a convert to Judaism, declared: "America is stronger than the acts of a depraved bigot and anti-Semite." 

"This evil anti-Semitic attack is an assault on all of us," Trump told supporters at an election rally in Illinois where he drew loud cheers as he vowed to fully enforce the death penalty for such crimes.

"We must stand with our Jewish brothers and sisters to defeat anti-Semitism and vanquish the forces of hate."

Trump said he would soon travel to Pittsburgh in Pennsylvania, where hundreds held a candlelit vigil late on Saturday.

The president ordered all flags at the White House and at public grounds, military posts and naval stations to be flown at half-staff through 31 October as a mark of "solemn respect" for the victims.

'Sickening'

Stephen Weiss, a 60-year-old member of the congregation, described hearing dozens of shots coming from the synagogue's front lobby.

"We had services going on in the chapel when we heard a loud noise," he told the Tribune-Review newspaper. "I recognized it as gunshots."

Authorities said Bowers was armed with an assault rifle and at least three handguns when he opened fire shortly before 10:00 am (1400 GMT)  - leaving a scene described as "horrific" by Wendell Hissrich, Pittsburgh's public safety director.

"One of the worst that I've seen. I've been on plane crashes," said Hissrich, who confirmed that 11 people were killed, and six injured. No children were among the casualties. 

"It's sickening. Outside of just the evil factor of it, who wakes up on a Saturday morning to do that?" said Pittsburgh chef Nathan, 42, who came to pay his respects but refused to give his second name.

"Hate Has No Home Here," read a placard in a simple memorial, next to a heart-shaped US flag - the same slogan repeated in Hebrew and Arabic, with candles and bouquets of pink roses and carnations.

The United States is witnessing a sharp spike in anti-Semitic incidents, surging 57 percent from 2016 to 2017, to 1,986 from 1,267, according to the Anti-Defamation League, a civil rights group which has tracked anti-Semitism in the United States since the 1970s.

The ADL said it believes the Pittsburgh shooting to be the deadliest such attack in US history.

"Our hearts break for the victims, their families, and the entire Jewish community," said the group's head Jonathan Greenblatt. 

Bowers, who the FBI said was not previously known to law enforcement, appeared to be the author of a rash of anti-Semitic online posts, notably on the Gab.com website, where conspiracy theories are common.

'Toxic place to live'

A quote atop the Bowers page said "jews are the children of satan," according to screenshots of the now-suspended account released by the SITE Intelligence Group, which monitors extremist movements.

Saturday's attack comes at a time of heightened tensions - a day after a Trump supporter from Florida was arrested for mailing explosive devices to Democrats and liberals, setting the country on edge ahead of close-fought elections on 6 November.

Trump has been accused of fuelling hate with divisive rhetoric.

"I think our president's totally dividing us," agreed Nathan, the chef who came to pay his respects after getting off work close to the attack scene in Pittsburgh.

"He's created this and between what happened with the bombs last week and then this, if he doesn't take some type of responsibility, shame on him. He's making our place a very toxic place to live."

The attack drew condemnation and messages of solidarity from world leaders, with Israeli Prime Minister Binyamin Netanyahu declaring himself "heartbroken and appalled."

German Chancellor Angela Merkel slammed an act of "blind anti-Semitic hatred."

UN Secretary General Antonio Guterres called for a united front "to roll back the forces of racism, anti-Semitism, Islamophobia and other forms of hatred."

The Tree of Life Synagogue, whose congregation was founded more than 150 years ago, is located in the Squirrel Hill neighbourhood that is historically the heart of Jewish life in greater Pittsburgh.

Neighbours in the quiet, peaceful well-heeled neighbourhood came out of their homes to provide police with coffee to stave off the drizzle as officers manned road blocks, sealing off all approaches to the scene.

A 2017 Brandeis University study found that more than 80 percent of its residents were concerned about rising anti-Semitism.