diff --git a/moto/s3/responses.py b/moto/s3/responses.py
index 29a0c632..d602a567 100644
--- a/moto/s3/responses.py
+++ b/moto/s3/responses.py
@@ -943,13 +943,10 @@ class ResponseObject(_TemplateEnvironmentMixin, ActionAuthenticatorMixin):
             key_name = object_["Key"]
             version_id = object_.get("VersionId", None)
 
-            success, _ = self.backend.delete_object(
+            self.backend.delete_object(
                 bucket_name, undo_clean_key_name(key_name), version_id=version_id
             )
-            if success:
-                deleted_objects.append((key_name, version_id))
-            else:
-                error_names.append(key_name)
+            deleted_objects.append((key_name, version_id))
 
         return (
             200,
diff --git a/tests/test_s3/test_s3.py b/tests/test_s3/test_s3.py
index 7a9f2d99..7391ffae 100644
--- a/tests/test_s3/test_s3.py
+++ b/tests/test_s3/test_s3.py
@@ -689,8 +689,7 @@ def test_delete_keys_invalid():
     # non-existing key case
     result = bucket.delete_keys(["abc", "file3"])
 
-    result.deleted.should.have.length_of(1)
-    result.errors.should.have.length_of(1)
+    result.deleted.should.have.length_of(2)
     keys = bucket.get_all_keys()
     keys.should.have.length_of(3)
     keys[0].name.should.equal("file1")
@@ -4215,6 +4214,22 @@ def test_delete_objects_with_url_encoded_key(key):
     assert_deleted()
 
 
+@mock_s3
+def test_delete_objects_unknown_key():
+    bucket_name = "test-moto-issue-1581"
+    client = boto3.client("s3", region_name=DEFAULT_REGION_NAME)
+    client.create_bucket(Bucket=bucket_name)
+    client.put_object(Bucket=bucket_name, Key="file1", Body="body")
+
+    s = client.delete_objects(
+        Bucket=bucket_name, Delete={"Objects": [{"Key": "file1"}, {"Key": "file2"}]}
+    )
+    s["Deleted"].should.have.length_of(2)
+    s["Deleted"].should.contain({"Key": "file1"})
+    s["Deleted"].should.contain({"Key": "file2"})
+    client.delete_bucket(Bucket=bucket_name)
+
+
 @mock_s3
 @mock_config
 def test_public_access_block():
diff --git a/tests/test_s3bucket_path/test_s3bucket_path.py b/tests/test_s3bucket_path/test_s3bucket_path.py
index a1bdc5b0..06ec9caf 100644
--- a/tests/test_s3bucket_path/test_s3bucket_path.py
+++ b/tests/test_s3bucket_path/test_s3bucket_path.py
@@ -315,8 +315,8 @@ def test_delete_keys_with_invalid():
 
     result = bucket.delete_keys(["abc", "file3"])
 
-    result.deleted.should.have.length_of(1)
-    result.errors.should.have.length_of(1)
+    result.deleted.should.have.length_of(2)
+    result.errors.should.have.length_of(0)
     keys = bucket.get_all_keys()
     keys.should.have.length_of(3)
     keys[0].name.should.equal("file1")