diff --git a/copy_test.go b/copy_test.go
index 02421524..4fd04772 100644
--- a/copy_test.go
+++ b/copy_test.go
@@ -1779,7 +1779,9 @@ func TestCopyGraph_WithOptions(t *testing.T) {
 	t.Run("MountFrom error", func(t *testing.T) {
 		root = descs[6]
 		dst := &countingStorage{storage: cas.NewMemory()}
-		opts = oras.CopyGraphOptions{}
+		opts = oras.CopyGraphOptions{
+			Concurrency: 1,
+		}
 		var numMountFrom atomic.Int64
 		e := errors.New("mountFrom error")
 		opts.MountFrom = func(ctx context.Context, desc ocispec.Descriptor) ([]string, error) {
@@ -1790,7 +1792,8 @@ func TestCopyGraph_WithOptions(t *testing.T) {
 			t.Fatalf("CopyGraph() error = %v, wantErr %v", err, e)
 		}
 
-		if got, expected := dst.numExists.Load(), int64(7); got != expected {
+		// with a very low probability, dst.numExists may be 3
+		if got, expected := dst.numExists.Load(), int64(4); got != expected {
 			t.Errorf("count(Exists()) = %d, want %d", got, expected)
 		}
 		if got, expected := dst.numFetch.Load(), int64(0); got != expected {
@@ -1799,7 +1802,7 @@ func TestCopyGraph_WithOptions(t *testing.T) {
 		if got, expected := dst.numPush.Load(), int64(0); got != expected {
 			t.Errorf("count(Push()) = %d, want %d", got, expected)
 		}
-		if got, expected := numMountFrom.Load(), int64(4); got != expected {
+		if got, expected := numMountFrom.Load(), int64(1); got != expected {
 			t.Errorf("count(MountFrom()) = %d, want %d", got, expected)
 		}
 	})
@@ -1828,7 +1831,9 @@ func TestCopyGraph_WithOptions(t *testing.T) {
 			}
 			return nil
 		}
-		opts = oras.CopyGraphOptions{}
+		opts = oras.CopyGraphOptions{
+			Concurrency: 1,
+		}
 		var numPreCopy, numPostCopy, numOnMounted, numMountFrom atomic.Int64
 		opts.PreCopy = func(ctx context.Context, desc ocispec.Descriptor) error {
 			numPreCopy.Add(1)
@@ -1851,7 +1856,7 @@ func TestCopyGraph_WithOptions(t *testing.T) {
 			t.Fatalf("CopyGraph() error = %v, wantErr %v", err, e)
 		}
 
-		if got, expected := dst.numExists.Load(), int64(7); got != expected {
+		if got, expected := dst.numExists.Load(), int64(4); got != expected {
 			t.Errorf("count(Exists()) = %d, want %d", got, expected)
 		}
 		if got, expected := dst.numFetch.Load(), int64(0); got != expected {
@@ -1860,13 +1865,13 @@ func TestCopyGraph_WithOptions(t *testing.T) {
 		if got, expected := dst.numPush.Load(), int64(0); got != expected {
 			t.Errorf("count(Push()) = %d, want %d", got, expected)
 		}
-		if got, expected := numMount.Load(), int64(4); got != expected {
+		if got, expected := numMount.Load(), int64(1); got != expected {
 			t.Errorf("count(Mount()) = %d, want %d", got, expected)
 		}
-		if got, expected := numOnMounted.Load(), int64(4); got != expected {
+		if got, expected := numOnMounted.Load(), int64(1); got != expected {
 			t.Errorf("count(OnMounted()) = %d, want %d", got, expected)
 		}
-		if got, expected := numMountFrom.Load(), int64(4); got != expected {
+		if got, expected := numMountFrom.Load(), int64(1); got != expected {
 			t.Errorf("count(MountFrom()) = %d, want %d", got, expected)
 		}
 		if got, expected := numPreCopy.Load(), int64(0); got != expected {
diff --git a/go.mod b/go.mod
index 85b83d90..bd267939 100644
--- a/go.mod
+++ b/go.mod
@@ -5,5 +5,5 @@ go 1.21
 require (
 	github.com/opencontainers/go-digest v1.0.0
 	github.com/opencontainers/image-spec v1.1.0
-	golang.org/x/sync v0.6.0
+	golang.org/x/sync v0.7.0
 )
diff --git a/go.sum b/go.sum
index 9b89e8ae..eec227b2 100644
--- a/go.sum
+++ b/go.sum
@@ -2,5 +2,5 @@ github.com/opencontainers/go-digest v1.0.0 h1:apOUWs51W5PlhuyGyz9FCeeBIOUDA/6nW8
 github.com/opencontainers/go-digest v1.0.0/go.mod h1:0JzlMkj0TRzQZfJkVvzbP0HBR3IKzErnv2BNG4W4MAM=
 github.com/opencontainers/image-spec v1.1.0 h1:8SG7/vwALn54lVB/0yZ/MMwhFrPYtpEHQb2IpWsCzug=
 github.com/opencontainers/image-spec v1.1.0/go.mod h1:W4s4sFTMaBeK1BQLXbG4AdM2szdn85PY75RI83NrTrM=
-golang.org/x/sync v0.6.0 h1:5BMeUDZ7vkXGfEr1x9B4bRcTH4lpkTkpdh0T/J+qjbQ=
-golang.org/x/sync v0.6.0/go.mod h1:Czt+wKu1gCyEFDUtn0jG5QVvpJ6rzVqr5aXyt9drQfk=
+golang.org/x/sync v0.7.0 h1:YsImfSBoP9QPYL0xyKJPq0gcaJdG3rInoqxTWbfQu9M=
+golang.org/x/sync v0.7.0/go.mod h1:Czt+wKu1gCyEFDUtn0jG5QVvpJ6rzVqr5aXyt9drQfk=
diff --git a/internal/syncutil/limit.go b/internal/syncutil/limit.go
index 2a05d4ea..3b28b8ed 100644
--- a/internal/syncutil/limit.go
+++ b/internal/syncutil/limit.go
@@ -17,6 +17,7 @@ package syncutil
 
 import (
 	"context"
+	"sync/atomic"
 
 	"golang.org/x/sync/errgroup"
 	"golang.org/x/sync/semaphore"
@@ -68,15 +69,24 @@ type GoFunc[T any] func(ctx context.Context, region *LimitedRegion, t T) error
 // Go concurrently invokes fn on items.
 func Go[T any](ctx context.Context, limiter *semaphore.Weighted, fn GoFunc[T], items ...T) error {
 	eg, egCtx := errgroup.WithContext(ctx)
+	var egErr atomic.Value
 	for _, item := range items {
-		region := LimitRegion(ctx, limiter)
+		region := LimitRegion(egCtx, limiter)
 		if err := region.Start(); err != nil {
+			if egErr, ok := egErr.Load().(error); ok && egErr != nil {
+				return egErr
+			}
 			return err
 		}
 		eg.Go(func(t T) func() error {
 			return func() error {
 				defer region.End()
-				return fn(egCtx, region, t)
+				// cancel the gorountine before the next goroutine is created
+				err := fn(egCtx, region, t)
+				if err != nil {
+					egErr.CompareAndSwap(nil, err)
+				}
+				return err
 			}
 		}(item))
 	}