San Francisco (CNN Business) The US Securities and Exchange Commission has rejected Elon Musk's claims that the regulator is unfairly trying to silence him.

In a filing Monday, the SEC said it was "stunning" that the billionaire business leader had continued to fire off tweets about Tesla without consulting others at the company despite having agreed to a court-ordered settlement requiring him to do so.

The filing is the latest salvo in a protracted battle between the SEC and Musk, who has been outspoken in his criticism of the securities regulator.

In the fall, Musk agreed to a court-approved deal with the SEC in order to settle charges over his controversial tweet in August about his plans to take Tesla private. The settlement stipulated that Musk receive pre-approval for any social media posts containing information that is "material" to Tesla shareholders. At the time, the electric carmaker said it would establish a board committee to oversee its CEO's posts.

But the SEC has since found fault with Musk's tweeting. In late February, the commission filed a motion asking a federal judge to hold Musk in contempt for violating the terms of the settlement.

The SEC cited a tweet from February 19 in which Musk said Tesla would build 500,000 cars in 2019. He then tweeted a clarifying message that Tesla would be building at an annual rate of 500,000 cars by the end of the year, but would actually only make 400,000 cars in 2019.

Musk fired back last week, arguing that the tweet didn't contain material information about Tesla, that he diligently tried to follow the court settlement, and that the SEC's request is a breach of his constitutional right to free speech.

'Reckless conduct'

The SEC disputed those points in its Monday filing.

"The pre-approval requirement was designed to protect against reckless conduct by Musk going forward," the agency said. "It is therefore stunning to learn that, at the time of filing of the [contempt] motion, Musk had not sought pre-approval for a single one of the numerous tweets about Tesla he published in the months since the court-ordered pre-approval policy went into effect."

Musk is interpreting the settlement "as not requiring pre-approval unless Musk himself unilaterally decides his planned tweets are material," the agency said, adding that such an approach is "inconsistent with the plain terms" of the settlement and makes the pre-approval requirement "meaningless."

The SEC also said that Musk has "made no diligent or good faith effort to comply with the pre-approval provision of the court's order."

And it dismissed the Tesla CEO's argument that his First Amendment rights are being violated because needing pre-approval for his tweets does not mean "that he is prohibited from speaking."

Tesla's TSLA stock is down 19% this year, yet investors sent the stock up slightly Tuesday after the SEC's rebuttal.

Lawyers representing Musk responded with a court filing seeking permission to address "unsupported assertions" made by the SEC and to submit documentation that "undermines" the regulator's position. Tesla didn't immediately respond to a request for comment.

The SEC sought to remove Musk as CEO of Tesla last year after he tweeted in August that he had secured funding to take the company private. It was eventually revealed that while he'd spoken with investors, he hadn't secured anything. The SEC said the tweet was "false and misleading."

The settlement allowed Musk to stay on as CEO, but he had to give up his role as chairman of Tesla. He and Tesla were fined a total of $40 million, which Musk paid himself.

The US District Court for Southern New York, which approved the original settlement in October, will decide whether Musk's February 19 tweet violated the deal.