diff --git a/packages/react-dom/src/client/ReactDOMHostConfig.js b/packages/react-dom/src/client/ReactDOMHostConfig.js
index b4fa2dd61b..cdea9f903b 100644
--- a/packages/react-dom/src/client/ReactDOMHostConfig.js
+++ b/packages/react-dom/src/client/ReactDOMHostConfig.js
@@ -897,18 +897,19 @@ export function mountEventComponent(
 ): void {
   if (enableEventAPI) {
     const rootContainerInstance = ((eventComponentInstance.rootInstance: any): Container);
-    const rootElement = rootContainerInstance.ownerDocument;
+    const doc = rootContainerInstance.ownerDocument;
+    const documentBody = doc.body || doc;
     const responder = eventComponentInstance.responder;
     const {rootEventTypes, targetEventTypes} = responder;
     if (targetEventTypes !== undefined) {
-      listenToEventResponderEventTypes(targetEventTypes, rootElement);
+      listenToEventResponderEventTypes(targetEventTypes, documentBody);
     }
     if (rootEventTypes !== undefined) {
       addRootEventTypesForComponentInstance(
         eventComponentInstance,
         rootEventTypes,
       );
-      listenToEventResponderEventTypes(rootEventTypes, rootElement);
+      listenToEventResponderEventTypes(rootEventTypes, documentBody);
     }
     mountEventResponder(eventComponentInstance);
   }
diff --git a/packages/react-events/src/Press.js b/packages/react-events/src/Press.js
index 6781c562f9..ecc3e807d1 100644
--- a/packages/react-events/src/Press.js
+++ b/packages/react-events/src/Press.js
@@ -37,6 +37,7 @@ type PressProps = {
     left: number,
   },
   preventDefault: boolean,
+  stopPropagation: boolean,
 };
 
 type PointerType = '' | 'mouse' | 'keyboard' | 'pen' | 'touch';
@@ -130,16 +131,18 @@ const rootEventTypes = [
   'pointermove',
   'scroll',
   'pointercancel',
+  // We listen to this here so stopPropagation can
+  // block other mouseup events used internally
+  {name: 'mouseup', passive: false},
+  'touchend',
 ];
 
 // If PointerEvents is not supported (e.g., Safari), also listen to touch and mouse events.
 if (typeof window !== 'undefined' && window.PointerEvent === undefined) {
   targetEventTypes.push('touchstart', 'mousedown');
   rootEventTypes.push(
-    {name: 'mouseup', passive: false},
     'mousemove',
     'touchmove',
-    'touchend',
     'touchcancel',
     // Used as a 'cancel' signal for mouse interactions
     'dragstart',
@@ -617,6 +620,9 @@ const PressResponder = {
     const nativeEvent: any = event.nativeEvent;
     const pointerType = context.getEventPointerType(event);
 
+    if (props.stopPropagation === true) {
+      nativeEvent.stopPropagation();
+    }
     switch (type) {
       // START
       case 'pointerdown':
@@ -740,6 +746,9 @@ const PressResponder = {
     const nativeEvent: any = event.nativeEvent;
     const pointerType = context.getEventPointerType(event);
 
+    if (props.stopPropagation === true) {
+      nativeEvent.stopPropagation();
+    }
     switch (type) {
       // MOVE
       case 'pointermove':
diff --git a/packages/react-events/src/__tests__/Press-test.internal.js b/packages/react-events/src/__tests__/Press-test.internal.js
index 044873dc60..0561154ce4 100644
--- a/packages/react-events/src/__tests__/Press-test.internal.js
+++ b/packages/react-events/src/__tests__/Press-test.internal.js
@@ -2591,4 +2591,22 @@ describe('Event responder: Press', () => {
       expect(onContextMenu).toHaveBeenCalledTimes(0);
     });
   });
+
+  it('should work correctly with stopPropagation set to true', () => {
+    const ref = React.createRef();
+    const element = (
+      <Press stopPropagation={true}>
+        <div ref={ref} />
+      </Press>
+    );
+    const pointerDownEvent = jest.fn();
+    container.addEventListener('pointerdown', pointerDownEvent);
+    ReactDOM.render(element, container);
+
+    ref.current.dispatchEvent(
+      createEvent('pointerdown', {pointerType: 'mouse', button: 0}),
+    );
+    container.removeEventListener('pointerdown', pointerDownEvent);
+    expect(pointerDownEvent).toHaveBeenCalledTimes(0);
+  });
 });