The victims' identities remain unknown and the synagogue was still cordoned off by police early on Sunday.
The US branch of the ZAKA International Rescue Unit said it was "waiting in the field for permission to enter the site to treat the bodies of the victims, which remain on the floor of the synagogue where they were murdered".
Candlelit vigils were held on Saturday night in Pittsburgh and outside the White House in Washington, DC.
Jonathan Greenblatt, the chief executive of the Anti-Defamation League, said: “Our hearts break for the families of those killed and injured at the Tree of Life Synagogue, and for the entire Jewish community of Pittsburgh.
“It is simply unconscionable for Jews to be targeted during worship on a Sabbath morning, and unthinkable that it would happen in the United States of America in this day and age.”
US media reported the suspect Robert Bowers wrote a social media post before the shooting railing against HIAS, a Jewish agency that resettles refugees.
"HIAS likes to bring in invaders to kill our people," he reportedly wrote.
"I can't sit by and watch our people get slaughtered. Screw your optics. I'm going in."
On his profile on Gab, a social media website favoured by the far right, Mr Bowers wrote the words "jews are the children of satan".
HIAS issued a statement saying: "There are no words to express how devastated we are by the events in Pittsburgh this morning.
"This loss is our loss, and our thoughts are with Tree of Life Congregation, our local partner Jewish Family and Community Services (JFCS) of Pittsburgh, the city of Pittsburgh and all those affected by this senseless act of violence.
"As we try to process this horrifying tragedy, we pray that the American Jewish community and the country can find healing."
The shul's website says it is home to a "conservative Jewish congregation" that "remains true to traditional teachings, yet is also progressive and relevant to the way we live today".
The website adds: "From our warm, inviting and intellectually stimulating atmosphere to our fun adult, children and family programs, it’s the perfect environment to grow a strong faith rooted in tradition."
Its building hosts services for three Jewish congregations, including the nearby New Light congregation.
Pittsburgh Public Safety Director Wendell Hissrich said the shooting was a hate crime, which means the FBI will lead the investigation.
“It’s a horrific crime scene, one of the worst I have seen,” he told reporters, adding police recovered an assault rifle and three handguns.
The Community Security Trust, which provides security to UK synagogues, said it was in contact with police and urged people to be "calm and vigilant" in light of "today's tragic shooting".
Board of Deputies President Marie van der Zyl said: "Our thoughts and prayers go out to the victims and families of the innocent worshippers gunned down in cold blood at a Pittsburgh synagogue.
"It is particularly chilling to hear reports that the shooter said 'all these Jews need to die'.
"The UK Jewish community stands in solidarity with everyone affected in the US."
The JLC said: "Our thoughts and prayers are with the Jewish community in Pittsburgh as they deal with the aftermath of the terrible events... which brought violence to a place and time of prayer.
"May the memory of those who were killed be blessed and may those who were injured achieve a full and rapid recovery."
Israel's Diaspora Minister Naftali Bennett tweeted he would head to Pittsburgh "to be with our brothers and sisters in their darkest hour".
"When Jews are murdered in Pittsburgh, the people of Israel feel the pain," he added.
Israeli Prime Minister Benjamin Netanyahu said: "I was heartbroken and appalled by the murderous attack on a Pittsburgh synagogue today.
"The entire people of Israel grieve with the families of the dead."
Speaking to reporters, Donald Trump denied the shooting showed the US needed tighter guns laws, saying: "This has little to do with it. If they had protection inside, the results would have been far better."
The president added: "If there was an armed guard inside they might have been able to stop him immediately. Maybe there would have been no-one killed except for him."
