diff --git a/.unreleased/pr_7673 b/.unreleased/pr_7673
new file mode 100644
index 000000000..703d9b92a
--- /dev/null
+++ b/.unreleased/pr_7673
@@ -0,0 +1,2 @@
+Fixes: #7673 Don't abort additional INSERTs when hitting first conflict
+Thanks: @bjornuppeke for reporting a problem with INSERT INTO ... ON CONFLICT DO NOTHING on compressed chunks
diff --git a/src/nodes/hypertable_modify.c b/src/nodes/hypertable_modify.c
index 54b7dbdf5..b49e9efc6 100644
--- a/src/nodes/hypertable_modify.c
+++ b/src/nodes/hypertable_modify.c
@@ -728,7 +728,7 @@ ExecModifyTable(CustomScanState *cs_node, PlanState *pstate)
 			cds->skip_current_tuple = false;
 			if (node->ps.instrument)
 				node->ps.instrument->ntuples2++;
-			return NULL;
+			continue;
 		}
 
 		/* No more tuples to process? */
diff --git a/tsl/test/expected/compression_conflicts.out b/tsl/test/expected/compression_conflicts.out
index f5f1a7e61..971c97234 100644
--- a/tsl/test/expected/compression_conflicts.out
+++ b/tsl/test/expected/compression_conflicts.out
@@ -748,3 +748,33 @@ VALUES
   (41, 1609478100000, 'val1')
 ON CONFLICT DO NOTHING;
 INFO:  Using index scan with scan keys: index 1, heap 4, memory 2. 
+INFO:  Using index scan with scan keys: index 1, heap 4, memory 2. 
+RESET timescaledb.debug_compression_path_info;
+-- gh issue #7672
+-- check additional INSERTS after hitting ON CONFLICT clause still go through
+CREATE TABLE test_i7672(time timestamptz, device text, primary key(time,device));
+SELECT create_hypertable('test_i7672', 'time');
+    create_hypertable     
+--------------------------
+ (13,public,test_i7672,t)
+(1 row)
+
+ALTER TABLE test_i7672 SET (timescaledb.compress, timescaledb.compress_orderby='time DESC', timescaledb.compress_segmentby='device');
+INSERT INTO test_i7672 VALUES ('2025-01-01','d1');
+SELECT count(*) FROM (SELECT compress_chunk(show_chunks('test_i7672'))) c;
+ count 
+-------
+     1
+(1 row)
+
+INSERT INTO test_i7672 VALUES
+('2025-01-01','d1'),
+('2025-01-01','d2')
+ON CONFLICT DO NOTHING;
+SELECT * FROM test_i7672 t ORDER BY t;
+             time             | device 
+------------------------------+--------
+ Wed Jan 01 00:00:00 2025 PST | d1
+ Wed Jan 01 00:00:00 2025 PST | d2
+(2 rows)
+
diff --git a/tsl/test/sql/compression_conflicts.sql b/tsl/test/sql/compression_conflicts.sql
index a54b9c67e..cbea58999 100644
--- a/tsl/test/sql/compression_conflicts.sql
+++ b/tsl/test/sql/compression_conflicts.sql
@@ -518,3 +518,21 @@ VALUES
   (41, 1609478100000, 'val1')
 ON CONFLICT DO NOTHING;
 
+RESET timescaledb.debug_compression_path_info;
+
+-- gh issue #7672
+-- check additional INSERTS after hitting ON CONFLICT clause still go through
+CREATE TABLE test_i7672(time timestamptz, device text, primary key(time,device));
+SELECT create_hypertable('test_i7672', 'time');
+ALTER TABLE test_i7672 SET (timescaledb.compress, timescaledb.compress_orderby='time DESC', timescaledb.compress_segmentby='device');
+INSERT INTO test_i7672 VALUES ('2025-01-01','d1');
+
+SELECT count(*) FROM (SELECT compress_chunk(show_chunks('test_i7672'))) c;
+
+INSERT INTO test_i7672 VALUES
+('2025-01-01','d1'),
+('2025-01-01','d2')
+ON CONFLICT DO NOTHING;
+
+SELECT * FROM test_i7672 t ORDER BY t;
+