SAN FRANCISCO (Reuters) - A federal judge on Thursday indicated a willingness to compel Elon Musk to testify again in the U.S. Securities and Exchange Commission's investigation into his $44 billion takeover of Twitter.

Lawyers for the billionaire appeared in a San Francisco courtroom on Thursday to urge U.S. District Judge Jacqueline Scott Corley to decide against the SEC, which is seeking to force Musk to testify as part of its probe into his 2022 purchase of social media giant Twitter. Another judge previously ruled in favor of the agency.

The SEC sued Musk in October to compel the Tesla and SpaceX CEO to testify after he refused to attend a September interview for the investigation, saying the SEC was trying to "harass" him with a number of subpoenas.

The judge did not issue a decision on Thursday.

"I don't think that the deposition subpoena is unreasonable. What I don't know is why does the deposition have to be at an SEC office?" Corley said at a hearing at the United States District Court for the Northern District of California.

The investigation concerns whether Musk broke federal securities laws in 2022 when he bought stock in Twitter, which he later renamed X. It is also reviewing statements and SEC filings he made in relation to the deal, the agency has previously said.

In 2022, Musk supplied the SEC with documents for its probe and also testified via videoconference for two half-day sessions in July of that year, the SEC has said in court documents. Agency lawyers have said they have more questions for Musk after receiving new documents, and had sought additional testimony.

Musk's lawyer, Rachel Frank, an associate with Quinn Emanuel Urquhart & Sullivan, on Thursday told the judge the additional testimony would be a "burden" for Musk and take him away from obligations to shareholders.

The judge asked whether Musk should be exempt from securities laws and further investigations just because he is a "very busy person" who is running multiple companies.

Musk did not immediately respond to a request for comment.

Thursday's face-off is the latest dispute in a years-long feud between Musk and the top U.S. markets regulator, dating back to 2018 when he tweeted that he had "funding secured" to take the electric carmaker private.