A federal judge gave Elon Musk and the Securities and Exchange Commission two weeks to resolve a dispute about whether Mr. Musk had violated a settlement he reached with the commission in October and should be held in contempt of court.

Judge Alison J. Nathan of Federal District Court in Manhattan told both sides to “take a deep breath” and put on “their reasonableness pants” after a roughly 90-minute hearing attended by Mr. Musk, the chief executive of the electric car company Tesla.

In Round 2 of the battle between the S.E.C. and Mr. Musk, the question for the judge came down to whether the voluble entrepreneur’s Twitter post on Feb. 19 about Tesla’s production figures violated the terms of the October settlement.

In the post, Mr. Musk said Tesla would produce about 500,000 cars in 2019. A month earlier, the company had said it would sell 360,000 to 400,000 cars this year. In a subsequent post, Mr. Musk said the company would in fact deliver about 400,000 cars in 2019.