"(Model 3) Production grows exponentially, so Aug should be 100 cars and Sept above 1,500," Musk said on Twitter. "Looks like we can reach 20,000 Model 3 cars per month in Dec."
"Expecting to complete SN1 on Friday," Mr Musk added.
SN1 is the first car off assembly line for sale, a person familiar with the matter confirmed to Reuters.
Mr Musk said in May Tesla was on track to begin production of the $35,000 Model 3 in July.
Tesla had said earlier, it expected to produce over 5,000 Model 3s per week by the end of this year and 10,000 vehicles per week "at some point in 2018".
Reuters reported in February that the electric carmaker had shut down production at its California assembly plant for a week for production of the Model 3 sedan, to meet its target of starting production in July.
Tesla's previous launches for its Model S sedan and Model X sports utility vehicle were hit by production delays and initial quality issues.
That track record meant some analysts were sceptical about the model's July launch.
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