Ousted Fox News host Tucker Carlson has announced he is launching a new show on Twitter.

The announcement came in a video on the social media site two weeks after his sudden exit from Fox News.

Carlson said: "You can't have a free society if people aren't allowed to say what they think is true."

Elon Musk said Twitter had not signed a deal with the host, who would be subject to the same rules as other "content creators".

On Tuesday, Carlson said he would be bringing a "new version" of his show to Twitter soon in a message captioned "we're back".

"Twitter has long served as the place where our national conversation incubates and develops," he says in the video.

"Twitter is not a partisan site, everybody's allowed here, and we think that's a good thing."

In April, Fox News announced in a brief statement that the network and Carlson had "agreed to part ways".

His last TV programme for the network had aired just days prior.

The 53-year-old was not just a popular presenter on Fox News - with more than three million viewers tuning in on an average night - but also a hugely influential one.

His shows frequently set the agenda for conservatives and, by extension, the Republican party.

Mr Musk retweeted Carlson's video on Tuesday evening, along with a statement saying: "On this platform, unlike the one-way street of broadcast, people are able to interact, critique and refute whatever is said.

"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."

The ex-Fox News host's comments follow his first public remarks in late April after he was forced out of the network.

In those remarks, he lashed out at "liars trying to silence" honest people.

He ended his comments saying: "Where can you still find Americans saying true things? There aren't many places left, but there are some."

The sudden announcement of Carlson's departure came shortly after Fox News paid $787m (£631m) to settle a defamation suit brought by voting machine company Dominion.

In the suit, Dominion argued its business was harmed by Fox spreading false claims that its machines had been rigged against former President Donald Trump. The case prompted disclosures of text messages that publicly aired Carlson's private views about Mr Trump and his colleagues at Fox.

The Wall Street Journal - owned by News Corp, which also owns Fox News - reported last month that his contract was worth about $20m a year.