Elon Musk started a public dispute with Apple on Monday.
In a series of Twitter entries, the new owner of the online platform complained about the electronics group.
Apple threatened to remove Twitter from its App Store without giving any reason.
The group has also largely stopped advertising on Twitter.
Musk directed one of his tweets directly at Apple CEO Tim Cook, asking him, "What's going on here?"
Business correspondent in New York.
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Musk suggested Apple wanted to censor Twitter.
"Do you hate free speech in America?" he asked, referring to the iPhone maker.
Musk also launched a Twitter poll, asking users if Apple should publicize any "censorship actions" it takes.
Musk and the secret Apple tax of 30 percent
Apple initially did not comment on Musk's allegations, so it remains unclear whether the company actually threatened to kick Twitter out of the App Store.
Apple boss Cook was asked in a television interview a few weeks ago what would have to happen for Apple to take a step.
He said he expects Twitter to continue to moderate content so it won't be necessary.
The question is relevant as Musk accused Twitter of excessive censorship prior to the purchase, and he has hinted that having him as the owner would allow for freer speech.
Musk has also implemented this and, for example, lifted the Twitter ban for former American President Donald Trump.
A few days ago, he said there should be a "general amnesty" for suspended users unless they violated the law or were highly responsible for "spam" content.
In the past, Apple and Google have often removed apps from their app stores due to insufficient moderation of content, such as the Parler service that competes with Twitter.
If the iPhone maker has actually largely stopped Twitter advertising, he would not be alone.
A number of companies have stopped posting ads on Twitter after being sold to Elon Musk, including automakers General Motors and Volkswagen and airline United Airlines.
Several major advertising agencies have advised their clients to pause Twitter ads.
Musk has publicly feuded with Apple before.
For example, he complained about the 30 percent commission that the company collects on revenue from apps, and described this as a "tax on the internet".
He also took up this criticism on Monday in his series of tweets.
He wrote, "Did you know that Apple charges a secret 30 percent tax on anything you buy from their App Store?"