Joe Biden, left, and Elon MuskJoe Biden, left, and Elon Musk

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

Musk said no one was watching Biden after the president did not mention the company in his speech.

Musk said in an email to CNBC that nobody is watching the State of the Union. The combined investments by Ford and GM are $18 billion. In Biden's address to the nation, there wasn't a mention ofTesla. CNBC's follow-up requests for comment were not immediately returned by Musk.

Musk said thatTesla has created over 50,000 US jobs building electric vehicles and is investing more than double GM and Ford combined.

CNBC reported on the ongoing battle between a billionaire and a commander in chief, but no mention was made by Biden. According to Forbes, Musk has a net worth of over $235 billion.

In an email exchange with CNBC, Musk said that if he was ever invited to a White House event, the administration had nothing to worry about. Musk has yet to attend a Biden White House meeting with other corporate leaders, including those featuring executives from Ford and GM.

According to people familiar with the matter, Biden and senior White House officials have told their allies that they have no plans to invite Musk to any upcoming meetings. The people were not named in order to speak freely about their private conversations.

Musk berated the president on the social networking site as recently as late January after Biden met with GM and Ford executives to discuss the president's "Build Back Better" initiative, which has been held up in Congress. Musk referred to Biden as a "damp sock puppet in human form".

More than half a dozen people familiar with the matter say that the president and his team are not happy with Musk's criticism.

According to a person familiar with the discussions, 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 hurt the president or the administration.