diff --git a/autotest/ogr/data/dxf/insert_only_col_count_zero.dxf b/autotest/ogr/data/dxf/insert_only_col_count_zero.dxf
new file mode 100644
index 000000000000..04b8de6fda85
--- /dev/null
+++ b/autotest/ogr/data/dxf/insert_only_col_count_zero.dxf
@@ -0,0 +1,200 @@
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diff --git a/autotest/ogr/ogr_dxf.py b/autotest/ogr/ogr_dxf.py
index 16cd74c362f8..9932e5288454 100644
--- a/autotest/ogr/ogr_dxf.py
+++ b/autotest/ogr/ogr_dxf.py
@@ -4124,3 +4124,24 @@ def test_ogr_dxf_write_MEASUREMENT(tmp_vsimem):
             pass
     with ogr.Open(filename) as ds:
         assert ds.GetMetadataItem("$MEASUREMENT", "DXF_HEADER_VARIABLES") == "     0"
+
+
+###############################################################################
+# Use case of https://github.com/OSGeo/gdal/issues/11591
+# Test reading a INSERT block whose column count is zero.
+# Not totally sure about the exact behavior we should do. Currently
+# the zero count is strictly honored and no geometry from the block will be
+# inserted into the regular geometries. LibreCAD 2.1.3 does the same thing
+
+
+@gdaltest.enable_exceptions()
+def test_ogr_dxf_insert_col_count_zero():
+
+    with ogr.Open("data/dxf/insert_only_col_count_zero.dxf") as ds:
+        lyr = ds.GetLayer(0)
+        assert lyr.GetFeatureCount() == 0
+
+    with gdal.config_option("DXF_INLINE_BLOCKS", "NO"):
+        with ogr.Open("data/dxf/insert_only_col_count_zero.dxf") as ds:
+            lyr = ds.GetLayerByName("blocks")
+            assert lyr.GetFeatureCount() == 1
diff --git a/ogr/ogrsf_frmts/dxf/ogrdxfdatasource.cpp b/ogr/ogrsf_frmts/dxf/ogrdxfdatasource.cpp
index 5c3d26b5e0df..cbdb9dd6173d 100644
--- a/ogr/ogrsf_frmts/dxf/ogrdxfdatasource.cpp
+++ b/ogr/ogrsf_frmts/dxf/ogrdxfdatasource.cpp
@@ -88,6 +88,8 @@ int OGRDXFDataSource::Open(const char *pszFilename, bool bHeaderOnly,
                            CSLConstList papszOptionsIn)
 
 {
+    SetDescription(pszFilename);
+
     osEncoding = CPL_ENC_ISO8859_1;
 
     bInlineBlocks = CPLTestBool(
diff --git a/ogr/ogrsf_frmts/dxf/ogrdxflayer.cpp b/ogr/ogrsf_frmts/dxf/ogrdxflayer.cpp
index 719d3bb85324..64aa386f81bc 100644
--- a/ogr/ogrsf_frmts/dxf/ogrdxflayer.cpp
+++ b/ogr/ogrsf_frmts/dxf/ogrdxflayer.cpp
@@ -3167,7 +3167,7 @@ bool OGRDXFLayer::TranslateINSERT()
 
             case 70:
                 m_oInsertState.m_nColumnCount = atoi(szLineBuf);
-                if (m_oInsertState.m_nColumnCount <= 0)
+                if (m_oInsertState.m_nColumnCount < 0)
                 {
                     DXF_LAYER_READER_ERROR();
                     m_oInsertState.m_nRowCount = 0;
@@ -3178,7 +3178,7 @@ bool OGRDXFLayer::TranslateINSERT()
 
             case 71:
                 m_oInsertState.m_nRowCount = atoi(szLineBuf);
-                if (m_oInsertState.m_nRowCount <= 0)
+                if (m_oInsertState.m_nRowCount < 0)
                 {
                     DXF_LAYER_READER_ERROR();
                     m_oInsertState.m_nRowCount = 0;
@@ -3205,6 +3205,12 @@ bool OGRDXFLayer::TranslateINSERT()
         return false;
     }
 
+    if (m_oInsertState.m_nRowCount == 0 || m_oInsertState.m_nColumnCount == 0)
+    {
+        m_oInsertState.m_nRowCount = 0;
+        m_oInsertState.m_nColumnCount = 0;
+    }
+
     /* -------------------------------------------------------------------- */
     /*      Process any attribute entities.                                 */
     /* -------------------------------------------------------------------- */