diff --git a/daemon/kill.go b/daemon/kill.go
index 1292f86b0c..5cde0d776d 100644
--- a/daemon/kill.go
+++ b/daemon/kill.go
@@ -4,10 +4,10 @@ import (
 	"context"
 	"fmt"
 	"runtime"
-	"strings"
 	"syscall"
 	"time"
 
+	"github.com/docker/docker/api/errdefs"
 	containerpkg "github.com/docker/docker/container"
 	"github.com/docker/docker/libcontainerd"
 	"github.com/docker/docker/pkg/signal"
@@ -97,15 +97,11 @@ func (daemon *Daemon) killWithSignal(container *containerpkg.Container, sig int)
 	}
 
 	if err := daemon.kill(container, sig); err != nil {
-		err = errors.Wrapf(err, "Cannot kill container %s", container.ID)
-		// if container or process not exists, ignore the error
-		// TODO: we shouldn't have to parse error strings from containerd
-		if strings.Contains(err.Error(), "container not found") ||
-			strings.Contains(err.Error(), "no such process") {
-			logrus.Warnf("container kill failed because of 'container not found' or 'no such process': %s", err.Error())
+		if errdefs.IsNotFound(err) {
 			unpause = false
+			logrus.WithError(err).WithField("container", container.ID).WithField("action", "kill").Debug("container kill failed because of 'container not found' or 'no such process'")
 		} else {
-			return err
+			return errors.Wrapf(err, "Cannot kill container %s", container.ID)
 		}
 	}
 
@@ -171,7 +167,7 @@ func (daemon *Daemon) Kill(container *containerpkg.Container) error {
 // killPossibleDeadProcess is a wrapper around killSig() suppressing "no such process" error.
 func (daemon *Daemon) killPossiblyDeadProcess(container *containerpkg.Container, sig int) error {
 	err := daemon.killWithSignal(container, sig)
-	if err == syscall.ESRCH {
+	if errdefs.IsNotFound(err) {
 		e := errNoSuchProcess{container.GetPID(), sig}
 		logrus.Debug(e)
 		return e
diff --git a/libcontainerd/client_daemon.go b/libcontainerd/client_daemon.go
index 0a3502c347..78b1412068 100644
--- a/libcontainerd/client_daemon.go
+++ b/libcontainerd/client_daemon.go
@@ -27,6 +27,7 @@ import (
 	"github.com/containerd/containerd/archive"
 	"github.com/containerd/containerd/cio"
 	"github.com/containerd/containerd/content"
+	"github.com/containerd/containerd/errdefs"
 	"github.com/containerd/containerd/images"
 	"github.com/containerd/containerd/linux/runctypes"
 	"github.com/containerd/typeurl"
@@ -317,7 +318,7 @@ func (c *client) SignalProcess(ctx context.Context, containerID, processID strin
 	if err != nil {
 		return err
 	}
-	return p.Kill(ctx, syscall.Signal(signal))
+	return wrapError(p.Kill(ctx, syscall.Signal(signal)))
 }
 
 func (c *client) ResizeTerminal(ctx context.Context, containerID, processID string, width, height int) error {
@@ -816,12 +817,19 @@ func (c *client) writeContent(ctx context.Context, mediaType, ref string, r io.R
 }
 
 func wrapError(err error) error {
-	if err != nil {
-		msg := err.Error()
-		for _, s := range []string{"container does not exist", "not found", "no such container"} {
-			if strings.Contains(msg, s) {
-				return wrapNotFoundError(err)
-			}
+	if err == nil {
+		return nil
+	}
+
+	switch {
+	case errdefs.IsNotFound(err):
+		return wrapNotFoundError(err)
+	}
+
+	msg := err.Error()
+	for _, s := range []string{"container does not exist", "not found", "no such container"} {
+		if strings.Contains(msg, s) {
+			return wrapNotFoundError(err)
 		}
 	}
 	return err