The letter from Apple was posted on

Twitter

TWTR -4.49%

by Mr. Buck, and it was confirmed by Mr. Lee’s office. Apple declined to comment. Parler didn’t immediately respond to requests for comment.

In the letter, Apple stood by its initial decision to remove Parler from the app store, citing posts that denigrated races and religions, promoted Nazi ideology and called for violence. Since January, Apple has had “substantial conversations” with Parler, and the app maker has proposed updates to its platform and its content-moderation policies, Apple said.

“The App Review Team has informed Parler as of April 14, 2021 that its proposed updated app will be approved for reinstatement to the App Store,” the letter said. The letter, which didn’t explain what changes Parler undertook, came in response to an inquiry that Messrs. Lee and Buck sent to Apple last month.

Mr. Buck said on Twitter that the decision was a “huge win for free speech.”

Parler LLC, which launched in 2018, landed in the middle of a debate about internet companies and free speech as it grew in popularity among supporters of then-President

Donald Trump.

Parler is similar in format to Twitter Inc.’s platform. Its rise coincided with more aggressive efforts on Twitter’s part to flag or remove content Twitter deemed objectionable or misleading. As of February, Parler said it had more than 20 million users, according to

Mark Meckler,

its interim chief executive.

Parler held itself out as a Twitter competitor that would take a hands-off approach moderating content. That policy made the platform an attractive online meeting place for the president’s supporters, who grew aggrieved at Twitter’s approach to content moderation as Mr. Trump disputed the results of the 2020 election and as Twitter eventually suspended his account.

Mr. Trump doesn’t have a Parler account, but conservative commentators such as

Sean Hannity

and Mark Levin have an active presence on the platform. Lawmakers who have given Mr. Trump strong support, including

Rep. Devin Nunes

of California and

Rep. Marjorie Taylor Greene

of Georgia, also have active accounts, as does Mr. Buck.

After the mob attack on the Capitol on Jan. 6, Apple and other big tech companies moved quickly to sever ties with Parler, which had given some people involved in the attack a forum for discussing their plans.

Amazon.com Inc.

AMZN -1.58%

suspended Parler from its web-hosting services.

Alphabet Inc.,

GOOG -1.11%

like Apple, also removed Parler from its app store.

In response to criticism that it served as a staging ground for the Capitol attack, Parler has said that it referred dozens of examples of violent content to the FBI in the weeks before the mob gathered in Washington.

Apple had previously denied an earlier attempt by Parler to seek reinstatement.

Evelyn Douek,

a Harvard Law School lecturer who studies content moderation, said that tech platforms, including Apple, need to provide clearer guidelines as to what content is acceptable.

“If Apple wants to get into the game of playing gatekeeper on the basis of content, it should be a lot more transparent about its requirements,” Ms. Douek said.

Parler has filed suit against Amazon for cutting off the web-hosting services, saying it did so for anticompetitive reasons. Parler in February gained limited functionality after securing internet services hosted by SkySilk Inc., which operates out of a Los Angeles-area data center. Users could access the service via a web browser or if they had previously installed the app on their mobile devices.

It remains off the Google Play store, and a Parler spokesman previously said that it wasn’t actively trying to restore the app to the store since it can be accessed other ways. Parler provides instructions on its website for users to install the app onto Android devices without going through the official app store.

A Google spokesman said that Parler could be available in the Google Play store once it submits an app that complies with its policies.

—Paul Ziobro contributed to this article.

Write to Matt Grossman at matt.grossman@wsj.com