Jassem said, "F*** you. I hope you die before you arrive in Syria."
Jaseem is said to be too ashamed to return to his job as a storekeeper after his son's identity was revealed last week.
He appeared drawn but did not display any signs of emotions when he visited his lawyer in Kuwait today, the BBC reported.
His lawyer said he was in a "state of shock" after being questioned by the Kuwaiti authorities about his son's actions.
A second colleague - who spoke anonymously to Kuwait's Qabbas newspaper - said: "All I know is that he was talking about his son whose behaviour he was not able to control. He was so tired and kept on repeating that my son is not a good son."
Other appalled relatives of Emwazi condemned his actions and said they would welcome his death.
A Kuwaiti cousin, who would not give his name, said: "We hate him. We hope he will be killed soon. This will be good news for our family."
Yesterday, it was revealed that Emwazi's mother Ghania screamed out in shock when she realised that her son was Jihadi John after watching a beheading video.
She was described as "absolutely devastated" when she discovered he had fled to Syria, and a friend said she had been "crying ever since".
"She keeps asking her friends to pray for her son, pray for him to come back and so on."
Jaseem was a member of the 'Bidoun' group of stateless people denied citizenship by countries in the Gulf.
He worked as a police officer in Kuwait until he found his loyalties questioned after Saddam Hussein's 1990-1 invasion of the Gulf State because his family was originally from Iraq.
His family was reportedly accused of collaborating with the Iraqi army during the seven-month occupation.
Mr Emwazi took his wife and his children to live in London in 1993. He was awarded British nationality in 2002 and returned to Kuwait the next year, the Arab Times reported.
It is not known when he settled in his native country, and he is thought to have regularly travelled back and forth between the UK and Kuwait.
Local sources say he has been living and working in Kuwait for at least two years.
MailOnline today visited a house in the dusty Kuwaiti suburb of Al-Ayoun said to be linked to the Emwazis.
But a Kuwaiti woman who answered the door said she had never heard of the family and insisted she had lived there for many years.
Meanwhile, it was also revealed today that Jihadi John is understood to have taken a bride in Syria after becoming Islamic State's most feared executioner.
A family friend said the masked butcher is believed to have married since joining the terror group in 2013.
It is unclear whether the British intelligence services are aware who his bride is.
But once she is identified, security chiefs will be desperate to investigate her and her family's background for clues that could help them locate the feared terrorist.
Emwazi, from Queen's Park, north-west London, was born in Kuwait in 1988 but moved to Britain with his parents and younger siblings in 1993 after the Gulf War.
He went to school and university in the UK before returning to Kuwait to work in 2009.
While living in the Gulf State, he became engaged to a local woman and found a job as a salesman for a computer software company.
Emwazi was banned from re-entering Kuwait in May 2010 after the British authorities raised concerns about his links to extremism.
He claimed this cost him his job and his fiancee in the Gulf State.
A family friend said Emwazi was thought to have married after joining Isis in Syria.
"I heard from a few friends that he had gone to fight, and when I asked a family member about it, she said, 'Oh he's moved to Syria to work and has gotten married'," he told The Times.
A video emerged this week which is believed to show Emwazi ranting on camera shortly after he arrived in Syria from the UK.
The footage is of two bands of fanatical fighters joining forces in 2013 under the command of notorious terrorist Omar al-Shishani.
At the front stands a man thought to be Emwazi - the west Londoner last week unmasked as the killer of Western hostages in a series of videos which have shocked the world.
New tapes also revealed today that the killer told MI5 he was a 'moderate Muslim' as he desperately tried explain why he had been picked up in terror-plagued east Africa.
Cage, the campaign group criticised for blaming the Isis killer's actions on Britain, released a recording of a 2009 interview they carried out with Emwazi.
In the recording, Emwazi tells how he was questioned by British security services after he was flown home from Tanzania suspected of trying to join Somali terror group al-Shabaab.
The Isis killer complained that he was being "threatened" by MI5 and moaned that agents were "putting words in his mouth".
But just three years after claiming he harboured no extremist tendencies, Emwazi appeared in Syria beheading Western hostages in violent Islamic State videos.
- Daily Mail