Twitter's Jack Dorsey posted a heart emoji above a screenshot of the App Store's top download chart, where Parler had been before the ban.
"Yeah, we were number one until the fake news rage mob at Twitter and your anti-competitive friends went after us," Parler's John Matze said.
The chief executives of Parler and Twitter were at odds with each other on Saturday, as each posted on their own network about Apple's ban of Parler.
After Apple banned Parler for failing to remove content promoting violence, Twitter CEO Jack Dorsey posted a picture of the Top Charts on the App Store.
On Parler, CEO John Matze responded by posting a screenshot of Dorsey's tweet and adding his own comment.
"Yeah, we were number one until the fake news rage mob at Twitter and your anti-competitive friends went after us," Matze wrote.
Matze said on Saturday the tech firms were working together to shut down Parler. »