The audio recording of Yair Netanyahu, who has been the subject of controversy in the past, led to further criticism of his father's handling of Israel's natural gas industry at a time when he already faces two unrelated graft investigations.
The conversation on the recording also includes talk of strippers and prostitutes.
Netanyahu's family denounced the broadcast of the recording by Israel's Channel 2 television late Monday as part of a witch-hunt, while Yair Netanyahu said he was obviously joking in the audio said to be from 2015.
Speaking before meeting with ambassadors from NATO countries, Netanyahu stressed his son had apologised for speaking foolishly about women and that he had known nothing about the gas deal he referenced.
"Yair didn't know about it," he said. "He didn't know anything about it, and what he said, he said under the influence of alcohol, in a tasteless joke with a friend. But he had no idea."
Yair Netanyahu, now 26, can be heard in the recording speaking with the son of Kobi Maimon, a stakeholder in a company that owns a share in Israel's offshore Tamar gas field.
"My dad arranged $20 billion for your dad -- you can give me 400 shekels ($116/97 euros)," he says.
Yair Netanyahu says his mother is calling him at one point.
At another point in the recording, someone else with them -- Roman Abramov, a representative of Australian billionaire James Packer -- says "God help us" if the conversation ever becomes public.
Yair Netanyahu issued a statement apologising and saying he was only joking about the gas deal while "under the influence of alcohol".
"These statements do not represent who I am nor the values on which I was raised," he said.
"Regarding what I said about the gas deal, it was a joke. Anyone with a bit of common sense understands that right away."
Netanyahu faced a difficult political battle over Israel's natural gas arrangements, with opponents saying they overly favour the companies involved.
Labour party leader Avi Gabbay said the recording was a "new stain on the corrupt gas deal".
There was also criticism over Yair Netanyahu's security arrangements, with at least two lawmakers calling for an investigation.
A security guard employed by the state purportedly accompanied Yair Netanyahu to the strip club.
'Everything Is Fair Game'
The Netanyahus in a statement said the broadcast of the recording was part of a "witch-hunt against the family that has reached an unprecedented low".
"Apparently, everything is fair game to attack the Netanyahu government and family, including using a secret and illegal recording of young men drinking alcohol," it said.
The statement also said Netanyahu had no relationship with Maimon and was not aware of Yair Netanyahu's friendship with his son.
It said the premier had met Maimon "once 10 years ago".
Netanyahu repeated this on Tuesday, while saying his efforts to develop the gas fields were always in Israel's best interests.
According to the family, the recording was made by a driver from the prime minister's office. Israeli media reported that the driver has long since resigned for unrelated reasons.
The recording was a new blow to Netanyahu, who is already facing two separate graft investigations.
Police are probing Netanyahu over allegations he received expensive gifts from wealthy supporters. He is also being investigated over an alleged deal he sought with a newspaper publisher for favourable coverage.
Netanyahu, who has been questioned by police seven times in the investigations, has repeatedly denied any wrongdoing.
Separately, his wife Sara Netanyahu faces a possible trial over alleged misuse of public funds. She also denies the allegations.
Netanyahu's effort to approve a natural gas framework to develop Israel's significant offshore deposits met stiff resistance from opposition politicians and public protests.
After protracted political and bureaucratic challenges to the framework, including objections from anti-trust officials, Israel's supreme court in March 2016 struck it down.
It was later revised and given final approval. Netanyahu argued on Tuesday that the framework had opened Israel's gas market to further competition to Maimon's detriment.
Yair Netanyahu has drawn controversy in the past, including over a bizarre Facebook post in September suggesting there was a conspiracy against his family. The post included a series of anti-Semitic images.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)