diff --git a/registry/remote/example_test.go b/registry/remote/example_test.go
index 370486d7..4af2f401 100644
--- a/registry/remote/example_test.go
+++ b/registry/remote/example_test.go
@@ -18,6 +18,7 @@ import (
 	"bytes"
 	"context"
 	"encoding/json"
+	"errors"
 	"fmt"
 	"io"
 	"net/http"
@@ -38,14 +39,18 @@ import (
 )
 
 const (
-	exampleRepositoryName   = "example"
-	exampleTag              = "latest"
-	exampleConfig           = "Example config content"
-	exampleLayer            = "Example layer content"
-	exampleUploadUUid       = "0bc84d80-837c-41d9-824e-1907463c53b3"
-	ManifestDigest          = "sha256:0b696106ecd0654e031f19e0a8cbd1aee4ad457d7c9cea881f07b12a930cd307"
-	ReferenceManifestDigest = "sha256:6983f495f7ee70d43e571657ae8b39ca3d3ca1b0e77270fd4fbddfb19832a1cf"
-	_                       = ExampleUnplayable
+	exampleRepositoryName                 = "example"
+	exampleTag                            = "latest"
+	exampleConfig                         = "Example config content"
+	exampleLayer                          = "Example layer content"
+	exampleUploadUUid                     = "0bc84d80-837c-41d9-824e-1907463c53b3"
+	ManifestDigest                        = "sha256:0b696106ecd0654e031f19e0a8cbd1aee4ad457d7c9cea881f07b12a930cd307"
+	ReferenceManifestDigest               = "sha256:6983f495f7ee70d43e571657ae8b39ca3d3ca1b0e77270fd4fbddfb19832a1cf"
+	referrersAPIUnavailableRepositoryName = "no-referrers-api"
+	referrerDigest                        = "sha256:21c623eb8ccd273f2702efd74a0abb455dd06a99987f413c2114fb00961ebfe7"
+	referrersTag                          = "sha256-c824a9aa7d2e3471306648c6d4baa1abbcb97ff0276181ab4722ca27127cdba0"
+	referrerIndexDigest                   = "sha256:7baac5147dd58d56fdbaad5a888fa919235a3a90cb71aaa8b56ee5d19f4cd838"
+	_                                     = ExampleUnplayable
 )
 
 var (
@@ -99,6 +104,15 @@ var (
 		ArtifactType: "example/manifest",
 		Digest:       digest.FromBytes(exampleManifestWithBlobs),
 		Size:         int64(len(exampleManifestWithBlobs))}
+	subjectDescriptor          = content.NewDescriptorFromBytes(ocispec.MediaTypeImageManifest, []byte(`{"layers":[]}`))
+	referrerManifestContent, _ = json.Marshal(ocispec.Manifest{
+		MediaType: ocispec.MediaTypeImageManifest,
+		Subject:   &subjectDescriptor,
+	})
+	referrerDescriptor = content.NewDescriptorFromBytes(ocispec.MediaTypeImageManifest, referrerManifestContent)
+	referrerIndex, _   = json.Marshal(ocispec.Index{
+		Manifests: []ocispec.Descriptor{},
+	})
 )
 
 var host string
@@ -205,6 +219,20 @@ func TestMain(m *testing.M) {
 			if m == "GET" {
 				w.Write([]byte(resultBlob))
 			}
+		case p == fmt.Sprintf("/v2/%s/referrers/%s", referrersAPIUnavailableRepositoryName, "sha256:0000000000000000000000000000000000000000000000000000000000000000"):
+			w.WriteHeader(http.StatusNotFound)
+		case p == fmt.Sprintf("/v2/%s/manifests/%s", referrersAPIUnavailableRepositoryName, referrerDigest) && m == http.MethodPut:
+			w.WriteHeader(http.StatusCreated)
+		case p == fmt.Sprintf("/v2/%s/manifests/%s", referrersAPIUnavailableRepositoryName, referrersTag) && m == http.MethodGet:
+			w.Write(referrerIndex)
+			w.Header().Set("Content-Type", ocispec.MediaTypeImageIndex)
+			w.Header().Set("Content-Length", strconv.Itoa(len(referrerIndex)))
+			w.Header().Set("Docker-Content-Digest", digest.Digest(string(referrerIndex)).String())
+			w.WriteHeader(http.StatusCreated)
+		case p == fmt.Sprintf("/v2/%s/manifests/%s", referrersAPIUnavailableRepositoryName, referrersTag) && m == http.MethodPut:
+			w.WriteHeader(http.StatusCreated)
+		case p == fmt.Sprintf("/v2/%s/manifests/%s", referrersAPIUnavailableRepositoryName, referrerIndexDigest) && m == http.MethodDelete:
+			w.WriteHeader(http.StatusMethodNotAllowed)
 		}
 
 	}))
@@ -785,3 +813,28 @@ func Example_tagReference() {
 	// Output:
 	// Tagged sha256:b53dc03a49f383ba230d8ac2b78a9c4aec132e4a9f36cc96524df98163202cc7 as latest
 }
+
+// Example_pushAndIgnoreReferrersIndexError gives example snippets on how to
+// ignore referrer index deletion error during push a referrer manifest.
+func Example_pushAndIgnoreReferrersIndexError() {
+	repo, err := remote.NewRepository(fmt.Sprintf("%s/%s", host, referrersAPIUnavailableRepositoryName))
+	if err != nil {
+		panic(err)
+	}
+	ctx := context.Background()
+
+	// push a referrer manifest and ignore cleaning up error
+	err = repo.Push(ctx, referrerDescriptor, bytes.NewReader(referrerManifestContent))
+	if err != nil {
+		var re *remote.ReferrersError
+		if !errors.As(err, &re) || !re.IsReferrersIndexDelete() {
+			panic(err)
+		}
+		fmt.Println("ignoring error occurred during cleaning obsolete referrers index")
+	}
+	fmt.Println("Push finished")
+
+	// Output:
+	// ignoring error occurred during cleaning obsolete referrers index
+	// Push finished
+}
diff --git a/registry/remote/referrers.go b/registry/remote/referrers.go
index ab307f71..75a1fa77 100644
--- a/registry/remote/referrers.go
+++ b/registry/remote/referrers.go
@@ -68,6 +68,38 @@ var (
 	errNoReferrerUpdate = errors.New("no referrer update")
 )
 
+const (
+	// opDeleteReferrersIndex represents the operation for deleting a
+	// referrers index.
+	opDeleteReferrersIndex = "DeleteReferrersIndex"
+)
+
+// ReferrersError records an error and the operation and the subject descriptor.
+type ReferrersError struct {
+	// Op represents the failing operation.
+	Op string
+	// Subject is the descriptor of referenced artifact.
+	Subject ocispec.Descriptor
+	// Err is the entity of referrers error.
+	Err error
+}
+
+// Error returns error msg of IgnorableError.
+func (e *ReferrersError) Error() string {
+	return e.Err.Error()
+}
+
+// Unwrap returns the inner error of IgnorableError.
+func (e *ReferrersError) Unwrap() error {
+	return errors.Unwrap(e.Err)
+}
+
+// IsIndexDelete tells if e is kind of error related to referrers
+// index deletion.
+func (e *ReferrersError) IsReferrersIndexDelete() bool {
+	return e.Op == opDeleteReferrersIndex
+}
+
 // buildReferrersTag builds the referrers tag for the given manifest descriptor.
 // Format: <algorithm>-<digest>
 // Reference: https://github.com/opencontainers/distribution-spec/blob/v1.1.0-rc1/spec.md#unavailable-referrers-api
diff --git a/registry/remote/repository.go b/registry/remote/repository.go
index 442d4464..5ded0a1e 100644
--- a/registry/remote/repository.go
+++ b/registry/remote/repository.go
@@ -1271,7 +1271,11 @@ func (s *manifestStore) updateReferrersIndex(ctx context.Context, subject ocispe
 		// 4. delete the dangling original referrers index
 		if !skipDelete {
 			if err := s.repo.delete(ctx, oldIndexDesc, true); err != nil {
-				return fmt.Errorf("failed to delete dangling referrers index %s for referrers tag %s: %w", oldIndexDesc.Digest.String(), referrersTag, err)
+				return &ReferrersError{
+					Op:      opDeleteReferrersIndex,
+					Err:     fmt.Errorf("failed to delete dangling referrers index %s for referrers tag %s: %w", oldIndexDesc.Digest.String(), referrersTag, err),
+					Subject: subject,
+				}
 			}
 		}
 		return nil