It is a transaction that will shift control of the social media platform populated by millions of users and global leaders to the world's richest person.
The Tesla CEO said the social media company needs to be taken private to grow and become a platform for free speech.
Speaking at a TED Talk in Vancouver when asked about his bid, Mr Musk said: "I think it's very important for there to be an inclusive arena for free speech."
Mr Musk made the bid last week in a letter to the board of Twitter – the micro-blogging platform that has become a global means of communication for individuals and world leaders.
It was made public in a regulatory filing on Thursday.
His offer price of $54.20 (£42) per share represents a 38 percent premium to Twitter's April 1 close, the last trading day before his 9.1 percent stake in the social media platform was made public.
Mr Musk, the world's richest person with a $273.6billion (£214billion) fortune according to a Forbes tally, rejected an invitation to join Twitter's board on Saturday after disclosing his stake, a move analysts said signaled his takeover intentions as a board seat would have limited his shareholding to just under 15 percent.
After his TED Talk, Mr Musk hinted at the possibility of a hostile bid in which he would bypass Twitter's board and put the offer directly to its shareholders, tweeting: "It would be utterly indefensible not to put this offer to a shareholder vote."
Twitter was evaluating the offer with guidance from Goldman Sachs and Wilson Sonsini Goodrich & Rosati, according to a source.
The company was also preparing a poison pill as a protective measure against Musk raising his stake as early as Friday, the source said.
Shares of Twitter closed down 1.7 percent on Thursday.
Investors were not convinced.
Saudi Arabia's Prince Alwaleed bin Talal tweeted from his verified account about the deal.
Describing himself as one of the "largest & long-term shareholders of Twitter," he said Mr Musk's offer undervalued the company and he rejected it.
Mr Musk told Twitter it was his "best and final offer" and said he would reconsider his investment if the board rejects it.
He added: "This is not a way to sort of make money."
Elon Musk
ALY SONG
Twitter
DADO RUVIC