An Israeli backpacker is among the rising number of dead following an earthquake that devastated the city of Christchurch on New Zealand's South Island, killing at least 75 people and razing many buildings, including the city's Chabad house.

The man, unofficially named as Ofer Mizrachi, from Kibbutz Magal, was crushed by a falling building while sitting in a car with three fellow nationals, who survived the incident.

The quake, measuring 6.3 on the Richter scale, ripped through the city on Tuesday lunch time.

At least 300 others were still missing on Tuesday night in what Prime Minister John Key - the son of a Jewish refugee who escaped Europe to England on the eve of the Holocaust - said could be the nation's "darkest day".

Three other Israelis who were known to be in the worst-hit area of the city at the time of the earthquake are also feared dead.

One Israeli backpacker was crushed by a falling building

Israel, which has hundreds of nationals trekking in the country every year, immediately offered to send food and medicine to help, and Magen David Adom is assessing the possibility of sending rescue personnel. The Foreign Ministry in Jerusalem believes there could be up to 150 Israelis in Christchurch.

Rabbi Shmuel Friedman, a New York-born emissary at the Chabad House in Christchurch, was inside the offices of the Jewish outreach centre with an Israeli backpacker when the first tremor jolted the city, just before 1pm local time.

"All of a sudden walls, ceilings started coming in on us, the shake was shifting us side to side," said Rabbi Friedman, who has been in the largest city on the South Island for less than three months.

"We just ran. I have no idea no idea how we managed to get out of there.

"There were many people in street in panic and shock; it was not a pretty scene. There were people running out of buildings, a lot of screaming, damage, smoke."

Amid the melee, he was unable to assess the damage to the building, but said it was unlikely to have survived the many aftershocks. The building also housed the city's only kosher café.

"The body is still in the car where the building collapsed," Rabbi Friedman said. "Emergency crews are still working on people who can be saved."

He said he gathered about 60 Israelis, including the three survivors from the car, in a square in the CBD, where he offered counselling and support.

"A group [of Israelis] went in to help evacuate people in buildings which were collapsing. They were experienced from the army," he said.

Around 2000 Jews live on South Island, and several families have had their homes destroyed, according to Rabbi Mendel Goldstein, the chief rabbi of Chabad in New Zealand.