More than 100 others were hurt during the Lag B'Omer event at Mount Meron in northern Israel, where annual commemorations include all-night prayers and dancing.
Four people remained in a critical condition on Friday afternoon, the country's health ministry said.
Prime Minister Benjamin Netanyahu said the victims would be remembered across the country on Sunday.
Chaotic scenes were captured on social media, showing men clambering through gaps in corrugated iron as they tried to escape the crush in the early hours of the morning.
"Masses of people were pushed into the same corner and a vortex was created," witness Dvir told Army Radio.
"I felt like I was about to die."
Casualties included children, some of whom became separated from their parents.
Attendee Shlomo Katz said: "We were standing and waiting for our friends - we were going to go inside for the dancing - and all of a sudden we saw paramedics running by, mid-CPR on kids."
Ambulances then began arriving "one after the other", he added.
Paramedic Omri Gorga said he saw "tens of people lying on the ground" and "tens of injured, walking and bleeding".
Speaking from a hospital bed, Avraham Leibe told Israeli public broadcaster Kan there was "general bedlam" on a slippery metal slope followed by stairs.
"Nobody managed to halt," he said. "I saw one after the other fall."
Areas were cordoned off to protect against COVID-19, and that may have produced unexpected bottlenecks, Israeli media said.
Mobile phone coverage around Mount Meron went down for several hours and emergency hotlines were overwhelmed with calls.
A pilgrim called Yitzhak told Channel 12 TV: "We thought maybe there was a (bomb) alert over a suspicious package.
"No one imagined that this could happen here. Rejoicing became mourning; a great light became a deep darkness."
Some 150 people were taken to hospital, said Zaki Heller, a spokesman for the Magen David Adom ambulance service.
"In one moment, we went from a happy event to an immense tragedy," he added.
Photographs show rows of wrapped bodies lying on the ground and dozens of ambulances.
Mobile intensive care units and helicopters were used to transport the most seriously injured to hospital.
"Close to 200 life-saving vehicles" were sent to the scene, emergency services spokesman Yoni Yagodozsky told Sky News, in addition to a "huge fleet" already there.
Mr Yagodozsky said the tragedy, which took place in a hilly area, happened while "people were on their way down from the main ceremony".
The path was narrow and "people tripped over", while those behind "simply walked on them and that's what created this horrible, horrible incident", he said.
Channel 13 TV showed photographs of seven boys and teenagers who may be missing.
While some of the deceased are yet to be identified, paramedic Uriel Goldberg told Sky News that most people had been accounted for by lunchtime on Friday.
The Haaretz newspaper quoted witnesses as saying police barricades had prevented people from exiting quickly.
The police's internal investigations department is looking at the conduct of officers, the Justice Ministry said.
Mr Yagodozsky said first responders are "well trained and well prepared" for these types of events, and had completed an exercise anticipating such a scenario.
"In the beginning, there was concern that one of the construction sets built in the area had collapsed. Then, it became more and more clear that people were trying to escape," he said.
There will be a "thorough investigation" following the "huge tragedy", Mr Yagodozsky added.
Funerals will be held before sundown on Friday - the start of the Jewish Sabbath, when burials do not take place.
Mr Netanyahu, who visited the site on Friday, described the incident as a "heavy disaster", adding: "We are all praying for the wellbeing of the casualties."
President Reuven Rivlin has lit memorial candles to honour the dead.
The Queen has sent a message of condolence to him, saying: "I was deeply saddened by news of the disaster at the Lag B'Omer festival in Meron, Israel.
"My thoughts are with all those who have been injured, and the friends and families of those who lost their lives. They have my deepest sympathies."
UK Prime Minister Boris Johnson described the incident as "devastating", tweeting: "My thoughts are with the Israeli people and those who have lost loved ones in this tragedy."
It is one of Israel's deadliest civilian events.
About 100,000 ultra-Orthodox Jews had gathered at the tomb of second-century sage Rabbi Shimon Bar Yochai, considered one of the holiest sites in the Jewish world.
Large crowds traditionally light bonfires, dance and pray.
It was the first large-scale religious festival since almost all Israel's coronavirus restrictions were lifted. In previous years, up to a quarter of a million people have attended.
The site is mostly gender-segregated and mobile-phone video suggests the crush took place mainly in the men's areas.
The gathering went ahead despite health officials warning that crowding could cause COVID to spread.
Israel has seen cases plummet since launching one of the world's most successful vaccination campaigns late last year.
More than 54% of the population has been fully inoculated.