A filing with the U.S. Securities and Exchange Commission (SEC) on Thursday showed that billionaire entrepreneur Elon Musk has made an offer to buy Twitter.

Musk has said he is willing to pay $54.20 per share to buy 100 percent of the company, and the all-cash offer will value the social network company at $43.4 billion.

"I invested in Twitter as I believe in its potential to be the platform for free speech around the globe," Musk wrote in an email to Bret Taylor, Twitter's board chairman. The email was reproduced in the SEC filing, adding that "Twitter needs to be transformed as a private company."

"My offer is my best and final offer and if it is not accepted, I would need to reconsider my position as a shareholder," Musk said. The offer was 54 percent premium over the day before he began investing in Twitter and 38 percent premium over the day before his investment was publicly announced.

Twitter released a statement confirming receipt of Musk's offer and saying its board will "carefully review the proposal to determine the course of action."

On April 4, Twitter confirmed that Musk had acquired a 9.2-percent share of the company to become its largest shareholder. But Musk later refused to join the board.

As a board member, Musk wouldn't be allowed to own more than 14.9 percent of the company.

According to Forbes, Musk is now the world's richest man, currently worth $273.6 billion. 

(With input from Xinhua)