Short answer
Check the merged manifest for the permission. If the app’s main purpose is not to send or receive app packages and let users install them, remove it, including when a library added it, and use Google Play for app updates. If it does qualify, fill in the Permissions Declaration Form in Play Console and describe the feature in the store listing.
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Why Google Play rejects the permission, and the fix
01
The app updates itself with a downloaded APK
“protecting users from apps that self update using any method other than Google Play's update mechanism or download harmful APKs.” Google Play, Use of the REQUEST_INSTALL_PACKAGES permission
A self-update flow that downloads and installs a new APK is the use Google Play is trying to stop. Remove it and use Google Play’s in-app updates instead, so updates come through the store.
02
A library added the permission
“an element in your merged manifest that you don't need that was provided by a lower-priority manifest file that's out of your control (such as an imported library)” Android Developers, Manage manifest files
An SDK or plugin, such as a file opener or an updater, can add the permission through manifest merging. Check the merged manifest in Android Studio, then remove the permission in your own manifest.
<manifest xmlns:android="http://schemas.android.com/apk/res/android" xmlns:tools="http://schemas.android.com/tools"> <uses-permission android:name="android.permission.REQUEST_INSTALL_PACKAGES" tools:node="remove" /> </manifest>03
Installing packages is not the app’s main purpose
“Permitted uses include: Web browsing or search; OR Communication services that support attachments; OR File sharing, transfer or management; OR Enterprise device management.” Google Play, Use of the REQUEST_INSTALL_PACKAGES permission
Google Play lists the permitted uses: the ones below, plus backup and restore, and device migration or phone transfer. An app outside them must remove the permission; a use not directly related to the app’s core purpose is not allowed.
04
The use qualifies but was not declared
“The core functionality, and any core features that comprise this core functionality, must all be prominently documented and promoted in the app's description.” Google Play, Use of the REQUEST_INSTALL_PACKAGES permission
A permitted app still needs the Permissions Declaration Form in Play Console, and the store description has to show the install feature.
05
The declaration no longer matches the app
Also check: a declaration filed for an older version goes stale when the feature changes. Update it in Play Console with the current use before the next release.
Checked against the vendor’s docs on : Google Play Help: Use of the REQUEST_INSTALL_PACKAGES permission; Android Developers: Manage manifest files; Android Developers: In-app updates.
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Related: Google Play QUERY_ALL_PACKAGES permission · Google Play photo and video permissions · Google Play prominent disclosure and consent · Google Play exact alarm permission