(Adds background on Musk)
By Alexandria Sage and Noel Randewich
SAN FRANCISCO, June 5 (Reuters) - Tesla Inc Chief Executive Elon Musk said on Tuesday that building 5,000 Model 3s per week by the end of June was "quite likely" as the company's production lines were now demonstrating the ability to make 3,500 vehicles per week.
"This is the most excruciating hellish several months I've ever had... but I think we're getting there," Musk said during Tesla's annual meeting of stockholders in Mountain View, California.
Musk's comments came after shareholders re-elected three directors and voted against a proposal to wrest the chairman role from Musk. That had represented the strongest challenge yet to Musk's grip on the Silicon Valley electric vehicle maker, which also faces production setbacks and expectations by many analysts that it will need to raise new cash.
Shares rose 1 percent after hours.
Tesla and its high-profile, tweeting CEO have been under the microscope in recent months after a spate of negative press over vehicle crashes, the company's cash position and the leadership style of Musk, who has snubbed financial analysts and publicly castigated the media.
Musk choked up after taking the microphone to talk about the company onstage in front of investors.
"At Tesla we build our cars with love," Musk said. "At a lot of other companies, they're built by marketing or the finance department and there's no soul. We're not perfect but we pour our heart and soul into it and we really care."
Tesla has been struggling to ramp up production of its new Model 3 sedan, which is crucial to the company's long-term profitability. In April, Tesla said it was making 2,270 vehicles a week, less than half the promised 5,000 a week it said it would meet by the end of June.
Manufacturing bottlenecks have delayed the delivery of vehicles to customers and deferred much-needed revenue as the company continues to spend heavily on Model 3 production fixes, as well as projects in the pipeline.
The company has been engaging in so-called "burst builds," temporary periods of fast-as-possible production which it uses to estimate how many cars it is capable of building over longer periods of time.
Analyst Brian Johnson of Barclays warned investors in March to be wary, however, of brief "burst rates" of Model 3 production that were not sustainable.
Musk has also come under fire for his behavior during an earnings conference call last month, in which he cut off analysts posing financial queries, rejecting them as "boring, bonehead questions." Shares fell as much as 7 percent after Musk's snub, evaporating $2 billion from Tesla's stock market value.
He repeated his assertion that the company was not planning on raising additional debt or equity, without providing a timeframe, and said he expected positive net income and cash flow in the third and fourth quarters.
Musk and another executive told investors that an announcement about a factory in Shanghai would come soon and talks were underway with the Chinese government.
Arguing that the sprawling company has become difficult to oversee, one investor proposed splitting the chairman and chief executive jobs, both of which Musk holds. Musk owns a 20 percent stake in the company.
Union-affiliated investment adviser CtW Investment Group had rallied shareholders to reject three Tesla directors it says lack qualifications or independence, including investor Antonio Gracias, Tesla's lead independent director; James Murdoch, the CEO of Twenty-First Century Fox Inc; and sustainable food executive Kimbal Musk, Elon Musk's brother.
Proxy firms Glass Lewis and Institutional Shareholder Services (ISS) and activist investor CtW Investment Group had supported separating the chairman and CEO roles and mostly opposed the three directors, the only ones up for election this year.
Tesla had recommended shareholders leave Musk with both top jobs and argued the directors are qualified.
Shares of Tesla are down nearly 8 percent from the beginning of the year and down 25 percent from a year high of $389.61 in September.
Reporting by Alexandria Sage and Noel Randewich in San Francisco; Editing by Lisa Shumaker