diff --git a/src/ol/format/WMTSCapabilities.js b/src/ol/format/WMTSCapabilities.js
index 9e72eb213e..9dceae171d 100644
--- a/src/ol/format/WMTSCapabilities.js
+++ b/src/ol/format/WMTSCapabilities.js
@@ -103,7 +103,7 @@ const LAYER_PARSERS = makeStructureNS(
   makeStructureNS(OWS_NAMESPACE_URIS, {
     'Title': makeObjectPropertySetter(readString),
     'Abstract': makeObjectPropertySetter(readString),
-    'WGS84BoundingBox': makeObjectPropertySetter(readWgs84BoundingBox),
+    'WGS84BoundingBox': makeObjectPropertySetter(readBoundingBox),
     'Identifier': makeObjectPropertySetter(readString),
   })
 );
@@ -196,6 +196,7 @@ const TMS_PARSERS = makeStructureNS(
   makeStructureNS(OWS_NAMESPACE_URIS, {
     'SupportedCRS': makeObjectPropertySetter(readString),
     'Identifier': makeObjectPropertySetter(readString),
+    'BoundingBox': makeObjectPropertySetter(readBoundingBox),
   })
 );
 
@@ -304,9 +305,9 @@ function readResourceUrl(node, objectStack) {
 /**
  * @param {Element} node Node.
  * @param {Array<*>} objectStack Object stack.
- * @return {Object|undefined} WGS84 BBox object.
+ * @return {Object|undefined} BBox object.
  */
-function readWgs84BoundingBox(node, objectStack) {
+function readBoundingBox(node, objectStack) {
   const coordinates = pushParseAndPop(
     [],
     WGS84_BBOX_READERS,
diff --git a/src/ol/source/WMTS.js b/src/ol/source/WMTS.js
index b56288bca8..4f73cfbcf0 100644
--- a/src/ol/source/WMTS.js
+++ b/src/ol/source/WMTS.js
@@ -9,7 +9,7 @@ import {assign} from '../obj.js';
 import {containsExtent} from '../extent.js';
 import {createFromCapabilitiesMatrixSet} from '../tilegrid/WMTS.js';
 import {createFromTileUrlFunctions, expandUrl} from '../tileurlfunction.js';
-import {equivalent, get as getProjection, transformExtent} from '../proj.js';
+import {equivalent, get as getProjection} from '../proj.js';
 import {find, findIndex, includes} from '../array.js';
 
 /**
@@ -479,27 +479,25 @@ export function optionsFromCapabilities(wmtsCap, config) {
     : matrix.TopLeftCorner;
   const tileSpanX = matrix.TileWidth * resolution;
   const tileSpanY = matrix.TileHeight * resolution;
-  let extent;
-  const wgs84BoundingBox = l['WGS84BoundingBox'];
-  const tileMatrixExtend = [
+  const matrixSetExtent = matrixSetObj['BoundingBox'];
+  let extent = [
     origin[0] + tileSpanX * selectedMatrixLimit.MinTileCol,
     // add one to get proper bottom/right coordinate
     origin[1] - tileSpanY * (1 + selectedMatrixLimit.MaxTileRow),
     origin[0] + tileSpanX * (1 + selectedMatrixLimit.MaxTileCol),
     origin[1] - tileSpanY * selectedMatrixLimit.MinTileRow,
   ];
-  if (wgs84BoundingBox !== undefined) {
+
+  if (
+    matrixSetExtent !== undefined &&
+    !containsExtent(matrixSetExtent, extent)
+  ) {
+    const wgs84BoundingBox = l['WGS84BoundingBox'];
     const wgs84ProjectionExtent = getProjection('EPSG:4326').getExtent();
+    extent = matrixSetExtent;
     wrapX =
       wgs84BoundingBox[0] === wgs84ProjectionExtent[0] &&
       wgs84BoundingBox[2] === wgs84ProjectionExtent[2];
-    extent = transformExtent(wgs84BoundingBox, 'EPSG:4326', projection);
-
-    if (!containsExtent(tileMatrixExtend, extent)) {
-      extent = tileMatrixExtend;
-    }
-  } else {
-    extent = tileMatrixExtend;
   }
 
   if (projection.getExtent() === null) {