The claim presented in the documentary is based on years of research by world-renowned archaeologists, statisticians, experts in ancient scripts and in DNA, the Israeli Yediot Ahronot daily Friday quoted the makers as saying in an exclusive interview.
The documentary, titled "The Burial Cave of Jesus," is a joint production by Israeli-born Canadian documentary maker Simcha Jacobovici and three-time-Oscar-winning Canadian film director James Cameron (Titanic, The Terminator).
The 2000-year-old cave had already been discovered in 1980 in Jerusalem's Talpiyot neighbourhood. In it were 10 coffins, six of which bore inscriptions, which - translated into English - included the names "Jesus son of Joseph," twice "Maria," and "Judah son of Jesus."
The second Maria is hypothesized to be Maria Magdalene, while the tomb bearing the name Judah could indicate Jesus had a son.
If true, the find could be one of the most significant in the history of archeology and shake the Christian world.
But the senior Israeli archaeologist who thoroughly researched the tombs after their discovery, and at the time deciphered the inscriptions, cast serious doubt on it.
"It's a beautiful story but without any proof whatsoever," Professor Amos Kloner, who had published the findings of his research in the Israeli periodical Atigot in 1996, told Deutsche Presse-Agentur dpa Friday.
"The names that are found on the tombs are names that are similar to the names of the family of Jesus," he conceded.
"But those were the most common names found among Jews in the first centuries BCE and CE," he added.
Kloner dismissed the combination of names found in the cave as a "coincidence."
The Israel Antiquities Authority (IAA), which is keeping the caskets in its archive in the town of Beit Shemesh near Jerusalem, declined to comment on the documentary, saying it had not researched the caskets and that its duty was only to safeguard them.
The IAA nevertheless sent two of the caskets to the news conference in New York.
The documentary, which took three years to make, is to be broadcast on the World Discovery Channel, Britain's Channel 4, Canada's Vision and Israel's Channel 8, which participated in its production.