Elon Musk on Tuesday said he had not signed a deal with Tucker Carlson, hours after the fired Fox News host revealed he is relaunching his show on Twitter.

The ousted television host made the announcement in a three-minute video posted to his Twitter page on Tuesday, in which he slammed the mainstream media and said anyone who tries to tell the truth 'will be fired.'

Sources close to Carlson have previously said he is preparing for 'war' against the network as he fights to be released from his $25 million-a-year contract, which prevented him from joining rival networks or starting one of his own.

'The best you can hope for in the news business at this point is the freedom to tell the fullest truth that you can, but there are always limits,' Carlson told his fans. 

'If you bump up against those limits often enough you will be fired for it. That's not a guess, it's guaranteed.'

He posted the video along with a tweet saying: 'We're back.'

Musk, who bought Twitter in October, said he had not signed a deal with Carlson, and the host would generate his own revenue from advertising.

The announcement comes just days after it was revealed that Carlson had a conversation with Twitter chief Elon Musk about working together.

But Musk on Tuesday denied any special agreement had been reached with Carlson. 

'I also want to be clear that we have not signed a deal of any kind whatsoever. Tucker is subject to the same rules & rewards of all content creators,' Musk tweeted, in response to Carlson's video.

'Rewards means subscriptions and advertising revenue share (still working on software needed for latter), which is a function of how many people subscribe and the advertising views associated with his content.'