Elon Musk takes aim at President Biden after he fails to mention Tesla during State of the Union

The feud between President Joe Biden and Tesla CEO Elon Musk doesn't seem to be cooling anytime soon.

Musk said no one was watching Biden after the president did not mention Tesla during his hourlong State of the Union address on Tuesday.

"Nobody is watching the State of the Union," Musk said in an email to CNBC. Biden touted the combined $18 billion investments by Ford and GM to build electric vehicles. Tesla, an electric automaker giant, wasn't mentioned in Biden's speech to the nation. Musk did not immediately return CNBC's follow-up requests for comment.

Musk later tweeted directly to Biden saying "Tesla has created over 50,000 US jobs building electric vehicles & is investing more than double GM + Ford combined."

The lack of a mention by Biden leading into Musk's latest comments comes after CNBC reported on the ongoing battle between a billionaire and a commander in chief. Musk, who also runs space exploration company SpaceX, has an estimated net worth of over $235 billion, according to Forbes.

Musk previously told CNBC in an email exchange that "Biden has pointedly ignored Tesla" while noting that if he was ever invited to a White House event, that the administration had "nothing to worry about. I would do the right thing." Musk has yet to attend a Biden White House meeting with other corporate leaders, including those featuring executives from Ford and GM.

Biden and senior White House officials have privately signaled to their allies that they have no immediate plans to invite Musk to any upcoming meetings with senior executives, according to people familiar with the matter. These people declined to be named in order to speak freely about private conversations.

Musk has previously berated the president on Twitter, as recently as late January after Biden met with General Motors CEO Mary Barra and Ford Motor CEO Jim Farley in a briefing with other corporate leaders to discuss the president's Build Back Better initiative, which has stalled in Congress. Musk, in a tweet, called Biden a "damp sock puppet in human form."

Behind the scenes, the president and his team are aggravated with Musk's criticism, according to more than half a dozen people familiar with the matter.

Biden's advisors have privately pushed back against inviting Musk to future industry events, as they are concerned the outspoken executive will say something that could embarrass the president or the administration, according to a person familiar with the discussions.