diff --git a/changelog/fragments/1736002257-log-fleet-enroll-failure-status-code.yaml b/changelog/fragments/1736002257-log-fleet-enroll-failure-status-code.yaml
new file mode 100644
index 00000000000..54e04d76d2f
--- /dev/null
+++ b/changelog/fragments/1736002257-log-fleet-enroll-failure-status-code.yaml
@@ -0,0 +1,32 @@
+# Kind can be one of:
+# - breaking-change: a change to previously-documented behavior
+# - deprecation: functionality that is being removed in a later release
+# - bug-fix: fixes a problem in a previous version
+# - enhancement: extends functionality but does not break or fix existing behavior
+# - feature: new functionality
+# - known-issue: problems that we are aware of in a given version
+# - security: impacts on the security of a product or a user’s deployment.
+# - upgrade: important information for someone upgrading from a prior version
+# - other: does not fit into any of the other categories
+kind: enhancement
+
+# Change summary; a 80ish characters long description of the change.
+summary: Added logger to print the status and code when enrollment call to fleet failed.
+
+# Long description; in case the summary is not enough to describe the change
+# this field accommodate a description without length limits.
+# NOTE: This field will be rendered only for breaking-change and known-issue kinds at the moment.
+#description:
+
+# Affected component; usually one of "elastic-agent", "fleet-server", "filebeat", "metricbeat", "auditbeat", "all", etc.
+component: elastic-agent
+
+# PR URL; optional; the PR number that added the changeset.
+# If not present is automatically filled by the tooling finding the PR where this changelog fragment has been added.
+# NOTE: the tooling supports backports, so it's able to fill the original PR number instead of the backport PR number.
+# Please provide it if you are adding a fragment for a different PR.
+#pr: https://github.com/owner/repo/1234
+
+# Issue URL; optional; the GitHub issue related to this changeset (either closes or is part of).
+# If not present is automatically filled by the tooling with the issue linked to the PR number.
+issue: https://github.com/elastic/elastic-agent/issues/6287
diff --git a/internal/pkg/agent/cmd/enroll_cmd.go b/internal/pkg/agent/cmd/enroll_cmd.go
index 91f652c9ef5..e25b03abb1c 100644
--- a/internal/pkg/agent/cmd/enroll_cmd.go
+++ b/internal/pkg/agent/cmd/enroll_cmd.go
@@ -524,21 +524,25 @@ func (c *enrollCmd) enrollWithBackoff(ctx context.Context, persistentConfig map[
 	}
 
 	c.log.Infof("1st enrollment attempt failed, retrying enrolling to URL: %s with exponential backoff (init %s, max %s)", c.client.URI(), enrollBackoffInit, enrollBackoffMax)
+
 	signal := make(chan struct{})
 	defer close(signal)
 	backExp := backoff.NewExpBackoff(signal, enrollBackoffInit, enrollBackoffMax)
 
 	for {
 		retry := false
-		if errors.Is(err, fleetapi.ErrTooManyRequests) {
+		switch {
+		case errors.Is(err, fleetapi.ErrTooManyRequests):
 			c.log.Warn("Too many requests on the remote server, will retry in a moment.")
 			retry = true
-		} else if errors.Is(err, fleetapi.ErrConnRefused) {
-			c.log.Warn("Remote server is not ready to accept connections, will retry in a moment.")
+		case errors.Is(err, fleetapi.ErrConnRefused):
+			c.log.Warn("Remote server is not ready to accept connections(Connection Refused), will retry in a moment.")
 			retry = true
-		} else if errors.Is(err, fleetapi.ErrTemporaryServerError) {
-			c.log.Warn("Remote server failed to handle the request, will retry in a moment.")
+		case errors.Is(err, fleetapi.ErrTemporaryServerError):
+			c.log.Warnf("Remote server failed to handle the request(%s), will retry in a moment.", err.Error())
 			retry = true
+		case err != nil:
+			c.log.Warnf("Enrollment failed: %s", err.Error())
 		}
 		if !retry {
 			break
diff --git a/internal/pkg/fleetapi/enroll_cmd.go b/internal/pkg/fleetapi/enroll_cmd.go
index 768b76cddfd..49ef33208fe 100644
--- a/internal/pkg/fleetapi/enroll_cmd.go
+++ b/internal/pkg/fleetapi/enroll_cmd.go
@@ -33,10 +33,10 @@ var ErrConnRefused = errors.New("connection refused")
 var ErrTemporaryServerError = errors.New("temporary server error, please retry later")
 
 // temporaryServerErrorCodes defines status codes that allow clients to retry their request.
-var temporaryServerErrorCodes = map[int]struct{}{
-	http.StatusBadGateway:         {},
-	http.StatusServiceUnavailable: {},
-	http.StatusGatewayTimeout:     {},
+var temporaryServerErrorCodes = map[int]string{
+	http.StatusBadGateway:         "BadGateway",
+	http.StatusServiceUnavailable: "ServiceUnavailable",
+	http.StatusGatewayTimeout:     "GatewayTimeout",
 }
 
 const (
@@ -223,8 +223,8 @@ func (e *EnrollCmd) Execute(ctx context.Context, r *EnrollRequest) (*EnrollRespo
 		return nil, ErrTooManyRequests
 	}
 
-	if _, temporary := temporaryServerErrorCodes[resp.StatusCode]; temporary {
-		return nil, fmt.Errorf("received code %d: %w", resp.StatusCode, ErrTemporaryServerError)
+	if status, temporary := temporaryServerErrorCodes[resp.StatusCode]; temporary {
+		return nil, fmt.Errorf("received status code %d (%s): %w", resp.StatusCode, status, ErrTemporaryServerError)
 	}
 
 	if resp.StatusCode != http.StatusOK {