diff --git a/src/connector/src/connector_common/postgres.rs b/src/connector/src/connector_common/postgres.rs
index d450c65f5ea5..1da128cfb545 100644
--- a/src/connector/src/connector_common/postgres.rs
+++ b/src/connector/src/connector_common/postgres.rs
@@ -73,6 +73,7 @@ impl PostgresExternalTable {
         table: &str,
         ssl_mode: &SslMode,
         ssl_root_cert: &Option<String>,
+        is_append_only: bool,
     ) -> ConnectorResult<Self> {
         tracing::debug!("connect to postgres external table");
         let mut options = PgConnectOptions::new()
@@ -140,8 +141,8 @@ impl PostgresExternalTable {
             column_descs.push(column_desc);
         }
 
-        if table_schema.primary_key_constraints.is_empty() {
-            return Err(anyhow!("Postgres table doesn't define the primary key").into());
+        if !is_append_only && table_schema.primary_key_constraints.is_empty() {
+            return Err(anyhow!("Postgres table should define the primary key for non-append-only tables").into());
         }
         let mut pk_names = vec![];
         table_schema.primary_key_constraints.iter().for_each(|pk| {
diff --git a/src/connector/src/sink/postgres.rs b/src/connector/src/sink/postgres.rs
index 2dce9bdd8038..f0f1aaf8fea2 100644
--- a/src/connector/src/sink/postgres.rs
+++ b/src/connector/src/sink/postgres.rs
@@ -166,6 +166,7 @@ impl Sink for PostgresSink {
                 &self.config.table,
                 &self.config.ssl_mode,
                 &self.config.ssl_root_cert,
+                self.is_append_only,
             )
             .await?;
 
@@ -414,7 +415,6 @@ impl PostgresSinkWriter {
                                 .await?;
                         }
                         Op::Delete => {
-                            unmatched_update_insert -= 1;
                             self.client
                                 .execute_raw(
                                     self.delete_statement.as_ref().unwrap(),
@@ -425,7 +425,9 @@ impl PostgresSinkWriter {
                                 )
                                 .await?;
                         }
-                        Op::UpdateDelete => {}
+                        Op::UpdateDelete => {
+                            unmatched_update_insert -= 1;
+                        }
                     }
                 }
             }
diff --git a/src/connector/src/source/cdc/external/mod.rs b/src/connector/src/source/cdc/external/mod.rs
index 871ea8b0f080..874e90bc4fc1 100644
--- a/src/connector/src/source/cdc/external/mod.rs
+++ b/src/connector/src/source/cdc/external/mod.rs
@@ -356,6 +356,7 @@ impl ExternalTableImpl {
                     &config.table,
                     &config.ssl_mode,
                     &config.ssl_root_cert,
+                    false,
                 )
                 .await?,
             )),
diff --git a/src/connector/src/source/cdc/external/postgres.rs b/src/connector/src/source/cdc/external/postgres.rs
index c79cd3ace277..091193f29c32 100644
--- a/src/connector/src/source/cdc/external/postgres.rs
+++ b/src/connector/src/source/cdc/external/postgres.rs
@@ -308,6 +308,7 @@ mod tests {
             &config.table,
             &config.ssl_mode,
             &config.ssl_root_cert,
+            false,
         )
         .await
         .unwrap();