diff --git a/plugins/repository-azure/src/internalClusterTest/java/org/elasticsearch/repositories/azure/AzureBlobStoreRepositoryTests.java b/plugins/repository-azure/src/internalClusterTest/java/org/elasticsearch/repositories/azure/AzureBlobStoreRepositoryTests.java
index b00936d3efa81..b62b83d7a971e 100644
--- a/plugins/repository-azure/src/internalClusterTest/java/org/elasticsearch/repositories/azure/AzureBlobStoreRepositoryTests.java
+++ b/plugins/repository-azure/src/internalClusterTest/java/org/elasticsearch/repositories/azure/AzureBlobStoreRepositoryTests.java
@@ -24,6 +24,7 @@
 import com.sun.net.httpserver.HttpExchange;
 import com.sun.net.httpserver.HttpHandler;
 import fixture.azure.AzureHttpHandler;
+import org.elasticsearch.common.Randomness;
 import org.elasticsearch.common.SuppressForbidden;
 import org.elasticsearch.common.blobstore.BlobContainer;
 import org.elasticsearch.common.blobstore.BlobPath;
@@ -39,14 +40,18 @@
 
 import java.io.IOException;
 import java.nio.charset.StandardCharsets;
+import java.util.ArrayList;
 import java.util.Base64;
 import java.util.Collection;
 import java.util.Collections;
+import java.util.List;
 import java.util.Map;
 import java.util.function.Predicate;
 import java.util.regex.Pattern;
 
+import static org.hamcrest.Matchers.anEmptyMap;
 import static org.hamcrest.Matchers.equalTo;
+import static org.hamcrest.Matchers.is;
 
 @SuppressForbidden(reason = "this test uses a HttpServer to emulate an Azure endpoint")
 public class AzureBlobStoreRepositoryTests extends ESMockAPIBasedRepositoryIntegTestCase {
@@ -231,4 +236,26 @@ public void testLargeBlobCountDeletion() throws Exception {
             assertThat(container.listBlobs().size(), equalTo(0));
         }
     }
+
+    public void testDeleteBlobsIgnoringIfNotExists() throws Exception {
+        try (BlobStore store = newBlobStore()) {
+            final BlobContainer container = store.blobContainer(new BlobPath());
+            List<String> blobsToDelete = new ArrayList<>();
+            for (int i = 0; i < 10; i++) {
+                byte[] bytes = randomBytes(randomInt(100));
+                String blobName = randomAlphaOfLength(10);
+                container.writeBlob(blobName, new BytesArray(bytes), false);
+                blobsToDelete.add(blobName);
+            }
+
+            // Try to delete non existent blobs
+            for (int i = 0; i < 10; i++) {
+                blobsToDelete.add(randomName());
+            }
+
+            Randomness.shuffle(blobsToDelete);
+            container.deleteBlobsIgnoringIfNotExists(blobsToDelete);
+            assertThat(container.listBlobs(), is(anEmptyMap()));
+        }
+    }
 }
diff --git a/plugins/repository-azure/src/internalClusterTest/java/org/elasticsearch/repositories/azure/AzureStorageCleanupThirdPartyTests.java b/plugins/repository-azure/src/internalClusterTest/java/org/elasticsearch/repositories/azure/AzureStorageCleanupThirdPartyTests.java
index a96522d451f3f..3997cf37b1f34 100644
--- a/plugins/repository-azure/src/internalClusterTest/java/org/elasticsearch/repositories/azure/AzureStorageCleanupThirdPartyTests.java
+++ b/plugins/repository-azure/src/internalClusterTest/java/org/elasticsearch/repositories/azure/AzureStorageCleanupThirdPartyTests.java
@@ -122,11 +122,4 @@ private void ensureSasTokenPermissions() {
         }));
         future.actionGet();
     }
-
-    @AwaitsFix(bugUrl = "https://github.com/elastic/elasticsearch/issues/66633")
-    @Override
-    // This override is only here so we can mute the test without muting the whole suite, remove it when the test is fixed
-    public void testCleanup() throws Exception {
-        super.testCleanup();
-    }
 }
diff --git a/plugins/repository-azure/src/main/java/org/elasticsearch/repositories/azure/AzureBlobStore.java b/plugins/repository-azure/src/main/java/org/elasticsearch/repositories/azure/AzureBlobStore.java
index e411552d6d10f..790d4563e99a2 100644
--- a/plugins/repository-azure/src/main/java/org/elasticsearch/repositories/azure/AzureBlobStore.java
+++ b/plugins/repository-azure/src/main/java/org/elasticsearch/repositories/azure/AzureBlobStore.java
@@ -275,24 +275,25 @@ void deleteBlobList(List<String> blobs) throws IOException {
                 List<Mono<Void>> deleteTasks = new ArrayList<>(blobs.size());
                 final BlobContainerAsyncClient blobContainerClient = asyncClient.getBlobContainerAsyncClient(container);
                 for (String blob : blobs) {
-                    deleteTasks.add(blobContainerClient.getBlobAsyncClient(blob).delete());
+                    final Mono<Void> deleteTask = blobContainerClient.getBlobAsyncClient(blob)
+                        .delete()
+                        // Ignore not found blobs
+                        .onErrorResume(e -> (e instanceof BlobStorageException) && ((BlobStorageException) e).getStatusCode() == 404,
+                            throwable -> Mono.empty());
+                    deleteTasks.add(deleteTask);
                 }
 
                 executeDeleteTasks(deleteTasks);
             });
-        } catch (BlobStorageException e) {
-            if (e.getStatusCode() != 404) {
-                throw new IOException("Unable to delete blobs " + blobs, e);
-            }
         } catch (Exception e) {
             throw new IOException("Unable to delete blobs " + blobs, e);
         }
     }
 
     private void executeDeleteTasks(List<Mono<Void>> deleteTasks) {
-        Flux.merge(deleteTasks)
-            .collectList()
-            .block();
+        // zipDelayError executes all tasks in parallel and delays
+        // error propagation until all tasks have finished.
+        Mono.zipDelayError(deleteTasks, results -> null).block();
     }
 
     public InputStream getInputStream(String blob, long position, final @Nullable Long length) throws IOException {
diff --git a/test/fixtures/azure-fixture/src/main/java/fixture/azure/AzureHttpHandler.java b/test/fixtures/azure-fixture/src/main/java/fixture/azure/AzureHttpHandler.java
index 9e53a9bc96e9c..7f0c259a4ed9d 100644
--- a/test/fixtures/azure-fixture/src/main/java/fixture/azure/AzureHttpHandler.java
+++ b/test/fixtures/azure-fixture/src/main/java/fixture/azure/AzureHttpHandler.java
@@ -152,8 +152,12 @@ public void handle(final HttpExchange exchange) throws IOException {
 
             } else if (Regex.simpleMatch("DELETE /" + account + "/" + container + "/*", request)) {
                 // Delete Blob (https://docs.microsoft.com/en-us/rest/api/storageservices/delete-blob)
-                blobs.entrySet().removeIf(blob -> blob.getKey().startsWith(exchange.getRequestURI().getPath()));
-                exchange.sendResponseHeaders(RestStatus.ACCEPTED.getStatus(), -1);
+                final boolean deleted = blobs.entrySet().removeIf(blob -> blob.getKey().startsWith(exchange.getRequestURI().getPath()));
+                if (deleted) {
+                    exchange.sendResponseHeaders(RestStatus.ACCEPTED.getStatus(), -1);
+                } else {
+                    exchange.sendResponseHeaders(RestStatus.NOT_FOUND.getStatus(), -1);
+                }
 
             } else if (Regex.simpleMatch("GET /" + account + "/" + container + "?*restype=container*comp=list*", request)) {
                 // List Blobs (https://docs.microsoft.com/en-us/rest/api/storageservices/list-blobs)