Israel's state comptroller on Monday announced the launch of an investigation into a stampede that killed 45 pilgrims at a religious festival, saying the crush "could have been prevented".

At least 16 children and teens were among those crushed to death in the early hours of Friday morning, a tragedy described as Israel's worst peacetime disaster.

Tens of thousands had packed a site at Mount Meron in northern Israel for the annual pilgrimage to the tomb of reputed second century rabbi Shimon Bar Yochai, coinciding with the Lag BaOmer holiday.

The tragedy "could have been prevented, and we must now determine how", Matanyahu Englman told journalists as he announced a "special audit" into the stampede.

Englman's office, a key government watchdog, had issued reports in 2008 and 2011 warning against the dangers to pilgrims at the Mount Meron site.

"The tomb of Rabbi Shimon Bar Yochai is not prepared properly to take in tens and hundreds of thousands of people who arrive for mass events," the 2008 report had said.

The later document said maintenance at the site was limited and numerous, illegally-built additions "were likely to endanger" people inside.

The stampede in the male section of the gender-divided site is believed to have started as people moved through a narrow passageway that became a deadly choke-point.

Israel held a national day of mourning Sunday following the tragedy at a mass pilgrimage
Israel held a national day of mourning Sunday following the tragedy at a mass pilgrimage AFP / Ahmad GHARABLI

Some blamed police for blocking access to a ramp that could have allowed pilgrims to escape.

Officials had authorised 10,000 pilgrims to attend this year, but several Israeli media outlets reported that 100,000 people showed up at Mount Meron. AFP could not confirm that figure.

Those killed were men and boys from the country's large ultra-Orthodox community. The Magen David Adom rescue agency said 120 people were also injured.

Prime Minister Benjamin Netanyahu pledged a full probe, but several people including Defence Minister Benny Gantz have demanded a state commission of inquiry, Israel's highest level of investigation.

Police chief for northern Israel Shimon Lavi said he was prepared to accept "responsibility", while Public Security Minister Amir Ohana, a close Netanyahu ally, said he was willing to face an inquiry.

"I'm responsible, but responsibility does not mean guilt," Ohana said.

On Monday one of the last victims, a 21-year-old Talmudic school student originally from Argentina, was laid to rest at a Jerusalem cemetery packed with hundreds of mourners, Israeli media reported.

The funerals and the identification of the dead, had started hours after the tragedy Friday but paused for the Sabbath, resuming when the Jewish day of rest ended at sundown Saturday.