Musk told investors in February that Tesla would produce 2,500 of the mass-market Model 3s per week by the end of the first quarter, and 5,000 per week by the end of the second quarter.
Shares gained 1.1% to $255.36 on Tuesday morning, and were as high as $271.33.
Tesla produced 2,020 Model 3s over the last seven days, according to the company. Tesla said it will produce 5,000 of the vehicles per week "in about three months," which is at least close to the prior guidance.
Musk originally targeted 5,000 Model 3s by the end of the 2017.
Tesla has had its share of bad news. Last week, the National Transportation Safety Board said it would investigate a fatal crash of a Tesla Model X vehicle in California. Also last week, company said it will recall 123,000 of its Model S sedans.
Tesla put a positive spin on the Model 3 production news on Tuesday.
Analysts expect Tesla will need to raise $2 billion to $3 billion within a year or so as it faces debt maturities and cash burn. A $230 million convertible bond maturity comes in November, and another $920 million comes due in March 2019.
But Tesla downplayed the need for capital on Tuesday. "Tesla does not require an equity or debt raise this year, apart from standard credit lines," the company said.