diff --git a/cmd/root.go b/cmd/root.go
index 9dbf0b963..4db15cf3b 100644
--- a/cmd/root.go
+++ b/cmd/root.go
@@ -463,6 +463,8 @@ the Proxy will then pick-up automatically.`)
 		"Enable debug logging")
 	localFlags.Uint64Var(&c.conf.MaxConnections, "max-connections", 0,
 		"Limit the number of connections. Default is no limit.")
+	localFlags.DurationVar(&c.conf.WaitBeforeClose, "min-sigterm-delay", 0,
+		"The number of seconds to accept new connections after receiving a TERM signal.")
 	localFlags.DurationVar(&c.conf.WaitOnClose, "max-sigterm-delay", 0,
 		"Maximum number of seconds to wait for connections to close after receiving a TERM signal.")
 	localFlags.StringVar(&c.conf.TelemetryProject, "telemetry-project", "",
@@ -1144,12 +1146,16 @@ func runSignalWrapper(cmd *Command) (err error) {
 	switch {
 	case errors.Is(err, errSigInt):
 		cmd.logger.Infof("SIGINT signal received. Shutting down...")
+		time.Sleep(cmd.conf.WaitBeforeClose)
 	case errors.Is(err, errSigTerm):
 		cmd.logger.Infof("SIGTERM signal received. Shutting down...")
+		time.Sleep(cmd.conf.WaitBeforeClose)
 	case errors.Is(err, errSigTermZero):
 		cmd.logger.Infof("SIGTERM signal received. Shutting down...")
+		time.Sleep(cmd.conf.WaitBeforeClose)
 	case errors.Is(err, errQuitQuitQuit):
 		cmd.logger.Infof("/quitquitquit received request. Shutting down...")
+		time.Sleep(cmd.conf.WaitBeforeClose)
 	default:
 		cmd.logger.Errorf("The proxy has encountered a terminal error: %v", err)
 	}
diff --git a/cmd/root_test.go b/cmd/root_test.go
index 027c2efff..4a4be698c 100644
--- a/cmd/root_test.go
+++ b/cmd/root_test.go
@@ -340,6 +340,13 @@ func TestNewCommandArguments(t *testing.T) {
 				MaxConnections: 1,
 			}),
 		},
+		{
+			desc: "using min-sigterm-delay flag",
+			args: []string{"--min-sigterm-delay", "10s", "proj:region:inst"},
+			want: withDefaults(&proxy.Config{
+				WaitBeforeClose: 10 * time.Second,
+			}),
+		},
 		{
 			desc: "using wait after signterm flag",
 			args: []string{"--max-sigterm-delay", "10s", "proj:region:inst"},
diff --git a/internal/proxy/proxy.go b/internal/proxy/proxy.go
index 26d32af74..d0eb3da82 100644
--- a/internal/proxy/proxy.go
+++ b/internal/proxy/proxy.go
@@ -170,6 +170,11 @@ type Config struct {
 	// connections. A zero-value indicates no limit.
 	MaxConnections uint64
 
+	// WaitBeforeClose sets the duration to wait after receiving a shutdown signal
+	// but before closing the process. Not setting this field means to initiate
+	// the shutdown process immediately.
+	WaitBeforeClose time.Duration
+
 	// WaitOnClose sets the duration to wait for connections to close before
 	// shutting down. Not setting this field means to close immediately
 	// regardless of any open connections.