Parler, a social network that pitches itself as a “free speech” alternative to Twitter and Facebook, is suffering from whiplash.

Over the past several months, Parler has become one of the fastest-growing apps in the United States. Millions of President Trump’s supporters have flocked to it as Facebook and Twitter increasingly cracked down on posts that spread misinformation and incited violence, including muzzling Mr. Trump by removing his accounts this past week. By Saturday morning, Apple listed Parler as the No. 1 free app for its iPhones.

But, by Saturday night, Parler was suddenly fighting for its life.

First, Apple and Google removed the app from their app stores because they said it had not sufficiently policed its users’ posts, allowing too many that encouraged violence and crime. Then, late Saturday, Amazon told Parler it would boot the company from its web-hosting service on Sunday night because of repeated violations of Amazon’s rules.

Amazon’s move meant that Parler’s entire platform would soon go offline unless it was able to find a new hosting service on Sunday.

“Big tech really wants to kill competition,” John Matze, Parler’s chief executive, said in a text message. “And I have a lot of work to do in the next 24 hours to make sure everyone’s data is not permanently deleted off the internet.”

A day earlier, Parler appeared poised to capitalize on growing anger at Silicon Valley in conservative circles and was even a logical choice to become Mr. Trump’s next megaphone after he was kicked off Twitter. Now its future is looking bleak.

In a letter to Parler on Saturday, Amazon said that it had sent the company 98 examples of posts on its site that encouraged violence and that many remained active. “It’s clear that Parler does not have an effective process to comply with” Amazon’s rules, the company said in the letter. Amazon “provides technology and services to customers across the political spectrum, and we continue to respect Parler’s right to determine for itself what content it will allow on its site. However, we cannot provide services to a customer that is unable to effectively identify and remove content that encourages or incites violence against others.”

On Friday, Apple gave Parler 24 hours to clean up its app or face removal from its App Store. Parler appeared to take down some posts over that period, but on Saturday, Apple told the company its measures were inadequate. “We have always supported diverse points of view being represented on the App Store, but there is no place on our platform for threats of violence and illegal activity,” Apple said in a statement.

“This is very huge,” Amy Peikoff, Parler’s policy chief, told Fox News after Apple gave its warning on Friday. Without access to the App Store, she said, “we’re toast.”