Tesla Inc. has again halted production of the Model 3 sedan, days after Chief Executive Elon Musk said the auto maker’s pace of making 2,000 of the sedans a week is sustainable.

The Silicon Valley company has fallen behind schedule in building its first mass-market car, missing several goals including a milestone of making 2,500 vehicles a week by the end of March. Further delays add more pressure for Tesla to crank up production to avoid squeezing its tight cash situation.

Tesla...