The newspaper said Musk alternated between laughter and tears during the interview in which he said he was working up to 120 hours a week and sometimes takes Ambien to get to sleep.
"This past year has been the most difficult and painful year of my career," he said. "It was excruciating."
The interview published Friday offered rare insights into Musk's personal life and thinking. He stood by his tweet last week saying he might take Tesla private and that he had secured the funding to do so.
Asked if he regretted it, he said, "Why would I?"
Musk has a reputation for being an eccentric visionary. But his out-of-the-blue announcement of a potential $72 billion (roughly Rs. 5 lakh crores) buyout of the publicly held company raised a huge ruckus and pushed Tesla's shares up 11 percent in a day, raising the company's value by $6 billion. They've fallen back but remain elevated.
The Wall Street Journal reported that government regulators have subpoenaed Tesla as they dig deeper into his disclosure of the potential buyout.
That signals regulators are investigating if Musk was truthful in the tweet about having the financing set for a deal that analysts have estimated would require $25 billion to $50 billion.
The company did not comment on that report, but it did say it was forming a special committee to evaluate proposals to take the company private.
The New York Times said that in response to questions for its article on the interview, Tesla issued a statement from its board, excluding Musk, that said "We would like to make it clear that Elon's commitment and dedication to Tesla is obvious."
In the interview with The New York Times, Musk said he fired off the tweet while on his way to the airport. He said his reference to having secured funding referred to a potential investment by Saudi Arabia's government investment fund.
Musk, 47, said sometimes he did not leave the Tesla factory for three or four days straight, and that he had not taken off more than a week at a time since he was sick with malaria in 2001.
Musk's social media antics have raised eyebrows as he berated analysts and falsely accused a cave diver of being a paedophile after the man was sceptical about a mini-submarine that Musk sent to possibly help rescue young soccer players from a flooded cave in Thailand. He later apologized for that remark.
The report cited people familiar with the situation as saying Tesla has been trying to find another top level executive to help relieve some of the pressure on Musk.
Musk said he did not intend to give up his roles as chairman and CEO but that if there was someone who could do the job better, "They can have the reins right now."
In a separate report, The Wall Street Journal said securities regulators have been investigating if Tesla misled investors about production problems for its Model 3 car.
The company could face sanctions if regulators find it misled investors about production delays.