In his internet posting, a man identified as Saad al-Mu'min said his friendship bestowed a protection on Johnson that other Muslims cannot violate. If Johnson was harmed, al-Mu'min told the captors on Thursday, "I will never forgive you. I will curse you in all my prayers."
Al-Mu'min added that Johnson, who works for Lockheed Martin on targeting and night vision systems for Apache helicopters, had expressed opposition to US foreign policy and an interest in converting to Islam.
"He was interested in reading Quran translations ... I swear to God that once he said to me in public, in a popular restaurant in Riyadh: 'I hate my country's politics. I am interested in Islam. If I convert, I will go and live with my wife in East Asia," al-Mu'min wrote. Johnson's wife is Thai.
"I want my father home"
Paul Johnson's son
Al-Mu'min said he was Johnson's 'colleague', but did not give any details about his job. He said he often invited Johnson over for dinner or and gave him books on Islam as gifts.
Site frequented by Islamists
The letter was posted late on Wednesday on websites where alleged al-Qaida members and other Islamists post messages.
Other contributors to the sites where the letter was posted ridiculed the message and called for Johnson's death.
Johnson's captors, believed linked to the anti-American network known as al-Qaida, have said they would kill him unless Saudi authorities release al-Qaida prisoners by Friday.
A US embassy official in the Saudi capital said that contacts with Saudi authorities were ongoing but would not comment further on the search for Johnson and/or his captors.
The hooded man is purported to
be the Saudi al-Qaida leader
Al-Mu'min, a pseudonym meaning "the believer", pointed to a saying by Islam's Prophet Muhammad: "If they were granted (Muslim) protection, then killing or taking their money or harming them is forbidden."
The group holding Johnson said in a video and a written statement, posted on a website on Tuesday, that Saudi authorities would have 72 hours to respond to their demands or he would be killed.
However, US Vice-President Dick Cheney said the US does not negotiate with 'hostage-takers.
"We do not, as a general proposition, believe it makes any sense to negotiate with hostage-takers," Cheney told CNBC television.
"If in fact the terrorists can come capture an American and
trade him for 12 of their own, who are in custody for their past murderous acts, then you will almost guarantee there will be further kidnappings," he said.
The 72 hours apparently ends sometime on Friday; the captors did not specify what time the countdown began or when it ends. Saudi newspapers on Thursday quoted unnamed government officials as saying the kingdom would not give in to the 'demands of terrorists'.
Johnson, a 49-year-old who had worked in Saudi Arabia for more than a decade, was seized on Saturday by a group calling itself al-Qaida in the Arabian Peninsula.
The organisation is believed to be headed by Abd al-Aziz Issa Abd al-Mohsin al-Moqrin, the top al-Qaida figure in Saudi Arabia.
In Johnson's home state of New Jersey, his son, Paul Johnson III, made a quiet plea for his father's safe return, telling The Associated Press: "I want my father home."
In an interview on NBC's "Today" show programme, Johnson said he had received no indication that authorities have made any progress in the search for his father.
Security has been increased in and around Riyadh as the search for Johnson continued.