Just recently, Tesla achieved a Model 3 production run rate exceeding 2,000 cars in a single, seven-day period. It took longer than expected to get there, but now the new target of 5,000 a week is in Musk's sight.

Once Tesla hits that 5,000 goal, the automaker will release new versions of the Model 3, according to Musk.

But there's still some work to be done before 5,000 Model 3s will roll off the line each week.