Americans on Sunday learned the identities of the 11 victims of the bloody assault on a Pittsburgh synagogue - a mostly elderly group and easy targets for a shooter who said he "wanted all Jews to die".

Nine of the 11 were 65 or older, several old enough to have been children during the rise of Nazism. They included Rose Mallinger, age 97, and couple Sylvan and Bernice Simon, both in their 80s.

Federal officials said on Sunday that 46-year-old suspect Robert Bowers - arrested at the Tree of Life synagogue after a firefight with police - faces 29 federal charges, many of them carrying the death penalty. He is to appear before a federal magistrate on Monday.

Across the country, prayer vigils and ecumenical services were held in tribute to the dead as words of solace and commiseration poured in from the US Jewish community - the largest outside Israel - but also from the pope and European leaders.

At a morning news conference, Allegheny County medical examiner Karl Williams described the grim work of identifying the dead with the help of grieving family members, supported by four rabbis working temporarily from his office.

The assault on the 150-year-old congregation was the deadliest anti-Semitic attack in recent US history.

The authorities described a 20-minute rampage that began when the gunman burst into the building early on Saturday and opened fire with an assault-style AR-15 rifle and two Glock handguns.

Four police officers or SWAT team members were injured, one critically. Bowers has been hospitalised in fair condition with multiple gunshot wounds.

Heightened tensions

President Donald Trump on Saturday solemnly denounced the attack, saying, "The scourge of anti-Semitism cannot be ignored, cannot be tolerated and cannot be allowed to continue."

Anti-Semitic acts in the United States rose sharply in recent years, Anti-Defamation League civil rights group that combats anti-Semitism figures show, by 34 per cent in 2016 over 2015, and by a further 57 per cent in 2016, "the single largest surge that we've ever seen" according to ADL director Jonathan Greenblatt.

Saturday's attack came 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 Nov 6.

Bowers lived in the Baldwin Borough suburb of Pittsburgh, less than half an hour's drive south of the Tree of Life synagogue.

He reportedly worked as a trucker, and has been linked to a rash of anti-Semitic online posts, notably on Gab.com, a site frequented by white nationalists, including one hours before the attack that called Jews "hostile invaders."

According to a criminal complaint filed Saturday, he told police he "wanted all Jews to die and that they (Jews) were committing genocide to his people."

- Bernama-NNN-Agencies