The first rollout of the subscription plan caused an uproar when many fake accounts popped up pretending to be celebrities or companies and Musk's team was forced to swiftly suspend the rollout.
The first try last month came just 10 days after Musk's $44 billion takeover of the influential platform and a mass round of layoffs that saw company staff levels halved, including teams of workers moderating content.
This time the company said that starting Monday subscribers would be required to be reviewed by Twitter before receiving the coveted blue check mark.
The checkmark will become gold for businesses and, later in the week, gray for government organizations, it added.
A blue checkmark on an account, which indicates it has been verified by Twitter, was previously free but reserved for organizations and public figures in an attempt to avoid impersonation and misinformation.
In the US relaunch, the Twitter Blue subscription service will cost $8 per month for users accessing Twitter on the web and $11 for those signing up on an Apple device.
The extra price for iPhone users could be explained by Musk's anger that Apple charges up to 30 percent service fee on the app store while banning other payment methods.
The relaunch of Twitter Blue comes as the Tesla and SpaceX owner has stepped up his tweets endorsing right-wing causes, including against the use of gender neutral pronouns and the US government's response to Covid-19.
Musk's free speech commitment has spooked away major advertisers, caught the attention of regulators and briefly challenged the company's access to the Apple app store.
Musk believes that the previous ownership of Twitter held a strong left-wing and pro-LGBT bias and unfairly banned accounts, including that of former president Donald Trump.
On Sunday he also lashed out against the outgoing key advisor of the US response to the Covid-19 pandemic, Anthony Fauci, a frequent target of vitriol on right-wing media.
Musk posted a meme showing Fauci telling US President Joe Biden, "Just one more lockdown, my king..."
Early in the pandemic, Musk tweeted that concern over the virus was "dumb" and since taking over Twitter has removed its policy targeting Covid misinformation.
His embrace of right-wing talking points seemed to attract increasing scorn in San Francisco, a politically liberal city and the headquarters for Twitter.
Musk was loudly booed by a crowd in San Francisco on Sunday night after he was invited on stage by comedian Dave Chappelle.
"It's almost as if I've offended San Francisco's unhinged leftists ... but nahhh," Musk tweeted after the event.