NEW YORK (Reuters) -The U.S. Securities and Exchange Commission (SEC) has extended its deadline until Monday for Elon Musk to respond to its offer to resolve an inquiry into the billionaire's $44-billion takeover of Twitter in 2022, a source familiar with the matter told Reuters.

On Thursday, Musk tweeted a copy of a letter sent by his lawyer to the chair of the SEC saying agency staff had given him 48 hours to agree to pay a penalty or face charges.

The SEC sent Musk a settlement offer on Tuesday seeking a response in 48 hours, but extended it to Monday after a request for more time, the source said.

The top U.S. markets regulator and Musk have been embroiled in a public court battle over the agency's investigation into his takeover of the social media platform, which Musk has since renamed X.

A spokesperson with the SEC's public affairs office declined to comment. Musk's lawyer did not respond immediately to calls for comment.

The SEC has been probing whether Musk broke securities laws in 2022 when he bought stock in Twitter, which Musk renamed X, as well as statements and filings he made in relation to the deal. It sought court enforcement of a subpoena to compel Musk's testimony on the matter.

The inquiry relates to Musk's late SEC filing regarding his Twitter stock purchases and whether he intended to benefit.