diff --git a/server/src/main/java/org/elasticsearch/repositories/blobstore/BlobStoreRepository.java b/server/src/main/java/org/elasticsearch/repositories/blobstore/BlobStoreRepository.java
index 2c71215c135ee..19b9e47c996ce 100644
--- a/server/src/main/java/org/elasticsearch/repositories/blobstore/BlobStoreRepository.java
+++ b/server/src/main/java/org/elasticsearch/repositories/blobstore/BlobStoreRepository.java
@@ -2740,6 +2740,15 @@ public boolean supportURLRepo() {
         return supportURLRepo;
     }
 
+    /**
+     * @return whether this repository performs overwrites atomically. In practice we only overwrite the `index.latest` blob so this
+     * is not very important, but the repository analyzer does test that overwrites happen atomically. It will skip those tests if the
+     * repository overrides this method to indicate that it does not support atomic overwrites.
+     */
+    public boolean hasAtomicOverwrites() {
+        return true;
+    }
+
     /**
      * The result of removing a snapshot from a shard folder in the repository.
      */
diff --git a/server/src/main/java/org/elasticsearch/repositories/fs/FsRepository.java b/server/src/main/java/org/elasticsearch/repositories/fs/FsRepository.java
index 30b7c935fbb16..746e6726f8ffe 100644
--- a/server/src/main/java/org/elasticsearch/repositories/fs/FsRepository.java
+++ b/server/src/main/java/org/elasticsearch/repositories/fs/FsRepository.java
@@ -103,4 +103,11 @@ protected BlobStore createBlobStore() throws Exception {
     protected ByteSizeValue chunkSize() {
         return chunkSize;
     }
+
+    @Override
+    public boolean hasAtomicOverwrites() {
+        // We overwrite a file by deleting the old file and then renaming the new file into place, which is not atomic.
+        // Also on Windows the overwrite may fail if the file is opened for reading at the time.
+        return false;
+    }
 }
diff --git a/x-pack/plugin/repository-encrypted/src/main/java/org/elasticsearch/repositories/encrypted/EncryptedRepository.java b/x-pack/plugin/repository-encrypted/src/main/java/org/elasticsearch/repositories/encrypted/EncryptedRepository.java
index b39a62c7c5e42..7944c20d351e7 100644
--- a/x-pack/plugin/repository-encrypted/src/main/java/org/elasticsearch/repositories/encrypted/EncryptedRepository.java
+++ b/x-pack/plugin/repository-encrypted/src/main/java/org/elasticsearch/repositories/encrypted/EncryptedRepository.java
@@ -379,6 +379,11 @@ private void validateLocalRepositorySecret(Map<String, Object> snapshotUserMetad
         }
     }
 
+    @Override
+    public boolean hasAtomicOverwrites() {
+        return delegatedRepository.hasAtomicOverwrites();
+    }
+
     // pkg-private for tests
     static final class EncryptedBlobStore implements BlobStore {
         private final BlobStore delegatedBlobStore;
diff --git a/x-pack/plugin/snapshot-repo-test-kit/src/main/java/org/elasticsearch/repositories/blobstore/testkit/BlobAnalyzeAction.java b/x-pack/plugin/snapshot-repo-test-kit/src/main/java/org/elasticsearch/repositories/blobstore/testkit/BlobAnalyzeAction.java
index 1bba56bdbd7f6..c975d855178b4 100644
--- a/x-pack/plugin/snapshot-repo-test-kit/src/main/java/org/elasticsearch/repositories/blobstore/testkit/BlobAnalyzeAction.java
+++ b/x-pack/plugin/snapshot-repo-test-kit/src/main/java/org/elasticsearch/repositories/blobstore/testkit/BlobAnalyzeAction.java
@@ -486,8 +486,6 @@ private void onReadsComplete(Collection<NodeResponse> responses, WriteDetails wr
                 if (response.isNotFound()) {
                     if (request.readEarly) {
                         nodeFailure = null; // "not found" is legitimate iff we tried to read it before the write completed
-                    } else if (request.writeAndOverwrite) {
-                        nodeFailure = null; // overwrites surprisingly not necessarily atomic, e.g. in a FsBlobContainer
                     } else {
                         nodeFailure = new RepositoryVerificationException(
                             request.getRepositoryName(),
diff --git a/x-pack/plugin/snapshot-repo-test-kit/src/main/java/org/elasticsearch/repositories/blobstore/testkit/RepositoryAnalyzeAction.java b/x-pack/plugin/snapshot-repo-test-kit/src/main/java/org/elasticsearch/repositories/blobstore/testkit/RepositoryAnalyzeAction.java
index 0e03e2c9f3aa0..b9b0c057fb5f3 100644
--- a/x-pack/plugin/snapshot-repo-test-kit/src/main/java/org/elasticsearch/repositories/blobstore/testkit/RepositoryAnalyzeAction.java
+++ b/x-pack/plugin/snapshot-repo-test-kit/src/main/java/org/elasticsearch/repositories/blobstore/testkit/RepositoryAnalyzeAction.java
@@ -465,7 +465,10 @@ public void run() {
                         request.getReadNodeCount(),
                         request.getEarlyReadNodeCount(),
                         smallBlob && random.nextDouble() < request.getRareActionProbability(),
-                        repository.supportURLRepo() && smallBlob && random.nextDouble() < request.getRareActionProbability()
+                        repository.supportURLRepo()
+                            && repository.hasAtomicOverwrites()
+                            && smallBlob
+                            && random.nextDouble() < request.getRareActionProbability()
                     )
                 );
                 queue.add(verifyBlobTask);