Two hours after pressing the launch button on Wednesday on Threads, Instagram’s new app for real-time, public conversations, Mark Zuckerberg posted that more than two million people had downloaded his latest creation. That was just the beginning. Another two hours later, five million people had downloaded Threads. By the time Mr. Zuckerberg, the chief executive of Meta, went to bed on Wednesday night, the number of downloads had soared to 10 million. When he woke on Thursday morning, the app had been downloaded more than 30 million times, he said.

In less than a day, Threads — which is aimed as a rival to Twitter — appears to have taken the crown as the most rapidly downloaded app ever. It easily outstripped ChatGPT, the chatbot, which was downloaded one million times within its first five days, according to OpenAI, ChatGPT’s maker. And Threads is on a pace to exceed 100 million users within two months, a feat achieved only by ChatGPT, according to the analytics firm Similarweb.

Some of Twitter’s most-followed users — such as Ellen DeGeneres, Bill Gates, Shakira and Oprah Winfrey — immediately joined Threads and began posting. The atmosphere was celebratory, with users writing welcome messages and expressing eagerness to read one another’s posts. At one point, the new app was so inundated with users that it appeared unstable.

“This is as good of a start as we could have hoped for!” Mr. Zuckerberg, whose company owns Instagram, Facebook, Messenger and WhatsApp, said in a post on Threads on Thursday. He later added, “Feels like the beginning of something special.”

The early momentum underscored people’s desire to find an alternative to Twitter, the 17-year-old digital town square that has long been the central place for public conversation online. Since Elon Musk bought Twitter last year, the billionaire has instituted changes that have angered the social platform’s longtime users, especially those who do not care for his laissez-faire approach to content moderation. Twitter has also suffered from more outages and bugs.

Mr. Musk isn’t taking Mr. Zuckerberg’s actions lying down. In a letter dated Wednesday, lawyers for Twitter threatened legal action against Meta, accusing it of using trade secrets from its former employees to build Threads. Twitter also asked Meta to preserve internal documents relevant to a dispute between the two companies. The letter was earlier reported by Semafor.

“Competition is fine, cheating is not,” Mr. Musk tweeted on Thursday.

Jack Dorsey, Twitter’s co-founder, also jabbed at Mr. Zuckerberg’s new app. “We wanted flying cars, instead we got 7 Twitter clones,” he tweeted on Thursday.