diff --git a/packages/react-events/src/Press.js b/packages/react-events/src/Press.js
index ddefbc3cb2..d6d76e6bbf 100644
--- a/packages/react-events/src/Press.js
+++ b/packages/react-events/src/Press.js
@@ -68,6 +68,7 @@ type PressState = {
     top: number,
   |}>,
   ignoreEmulatedMouseEvents: boolean,
+  allowPressReentry: boolean,
 };
 
 type PressEventType =
@@ -301,7 +302,6 @@ function dispatchPressEndEvents(
       deactivate(context, props, state);
     }
   }
-  removeRootEventTypes(context, state);
 }
 
 function isAnchorTagElement(eventTarget: EventTarget): boolean {
@@ -395,6 +395,7 @@ function unmountResponder(
   state: PressState,
 ): void {
   if (state.isPressed) {
+    removeRootEventTypes(context, state);
     dispatchPressEndEvents(context, props, state);
   }
 }
@@ -411,8 +412,11 @@ function dispatchCancel(
       (nativeEvent: any).preventDefault();
     } else {
       state.ignoreEmulatedMouseEvents = false;
+      removeRootEventTypes(context, state);
       dispatchPressEndEvents(context, props, state);
     }
+  } else if (state.allowPressReentry) {
+    removeRootEventTypes(context, state);
   }
 }
 
@@ -432,6 +436,7 @@ function removeRootEventTypes(
 ): void {
   if (state.addedRootEvents) {
     state.addedRootEvents = false;
+    state.allowPressReentry = false;
     context.removeRootEventTypes(rootEventTypes);
   }
 }
@@ -455,6 +460,7 @@ const PressResponder = {
       responderRegionOnActivation: null,
       responderRegionOnDeactivation: null,
       ignoreEmulatedMouseEvents: false,
+      allowPressReentry: false,
     };
   },
   stopLocalPropagation: true,
@@ -467,6 +473,7 @@ const PressResponder = {
     const {target, type} = event;
 
     if (props.disabled) {
+      removeRootEventTypes(context, state);
       dispatchPressEndEvents(context, props, state);
       state.ignoreEmulatedMouseEvents = false;
       return;
@@ -512,6 +519,7 @@ const PressResponder = {
             return;
           }
 
+          state.allowPressReentry = true;
           state.pointerType = pointerType;
           state.pressTarget = getEventCurrentTarget(event, context);
           state.responderRegionOnActivation = calculateResponderRegion(
@@ -565,7 +573,7 @@ const PressResponder = {
       case 'pointermove':
       case 'mousemove':
       case 'touchmove': {
-        if (state.isPressed) {
+        if (state.isPressed || state.allowPressReentry) {
           // Ignore emulated events (pointermove will dispatch touch and mouse events)
           // Ignore pointermove events during a keyboard press.
           if (state.pointerType !== pointerType) {
@@ -589,18 +597,24 @@ const PressResponder = {
           );
 
           if (state.isPressWithinResponderRegion) {
-            if (props.onPressMove) {
-              dispatchEvent(context, state, 'pressmove', props.onPressMove, {
-                discrete: false,
-              });
+            if (state.isPressed) {
+              if (props.onPressMove) {
+                dispatchEvent(context, state, 'pressmove', props.onPressMove, {
+                  discrete: false,
+                });
+              }
+            } else {
+              dispatchPressStartEvents(context, props, state);
             }
           } else {
+            if (!state.allowPressReentry) {
+              removeRootEventTypes(context, state);
+            }
             dispatchPressEndEvents(context, props, state);
           }
         }
         break;
       }
-
       // END
       case 'pointerup':
       case 'keyup':
@@ -635,6 +649,7 @@ const PressResponder = {
           }
 
           const wasLongPressed = state.isLongPressed;
+          removeRootEventTypes(context, state);
           dispatchPressEndEvents(context, props, state);
 
           if (state.pressTarget !== null && props.onPress) {
@@ -652,6 +667,8 @@ const PressResponder = {
           }
         } else if (type === 'mouseup' && state.ignoreEmulatedMouseEvents) {
           state.ignoreEmulatedMouseEvents = false;
+        } else if (state.allowPressReentry) {
+          removeRootEventTypes(context, state);
         }
         break;
       }
diff --git a/packages/react-events/src/__tests__/Press-test.internal.js b/packages/react-events/src/__tests__/Press-test.internal.js
index 1a5d44d86d..abf190025d 100644
--- a/packages/react-events/src/__tests__/Press-test.internal.js
+++ b/packages/react-events/src/__tests__/Press-test.internal.js
@@ -1148,6 +1148,193 @@ describe('Event responder: Press', () => {
         expect(events).toEqual([]);
       });
     });
+
+    it('"onPress" is not called on release with mouse', () => {
+      let events = [];
+      const ref = React.createRef();
+      const createEventHandler = msg => () => {
+        events.push(msg);
+      };
+
+      const element = (
+        <Press
+          onPress={createEventHandler('onPress')}
+          onPressChange={createEventHandler('onPressChange')}
+          onPressMove={createEventHandler('onPressMove')}
+          onPressStart={createEventHandler('onPressStart')}
+          onPressEnd={createEventHandler('onPressEnd')}>
+          <div ref={ref} />
+        </Press>
+      );
+
+      ReactDOM.render(element, container);
+
+      ref.current.getBoundingClientRect = getBoundingClientRectMock;
+      ref.current.dispatchEvent(
+        createPointerEvent('pointerdown', {
+          pointerType: 'mouse',
+        }),
+      );
+      ref.current.dispatchEvent(
+        createPointerEvent('pointermove', {
+          ...coordinatesInside,
+          pointerType: 'mouse',
+        }),
+      );
+      container.dispatchEvent(
+        createPointerEvent('pointermove', {
+          ...coordinatesOutside,
+          pointerType: 'mouse',
+        }),
+      );
+      container.dispatchEvent(
+        createPointerEvent('pointerup', {
+          ...coordinatesOutside,
+          pointerType: 'mouse',
+        }),
+      );
+      jest.runAllTimers();
+
+      expect(events).toEqual([
+        'onPressStart',
+        'onPressChange',
+        'onPressMove',
+        'onPressEnd',
+        'onPressChange',
+      ]);
+    });
+
+    it('"onPress" is called on re-entry to hit rect for mouse', () => {
+      let events = [];
+      const ref = React.createRef();
+      const createEventHandler = msg => () => {
+        events.push(msg);
+      };
+
+      const element = (
+        <Press
+          onPress={createEventHandler('onPress')}
+          onPressChange={createEventHandler('onPressChange')}
+          onPressMove={createEventHandler('onPressMove')}
+          onPressStart={createEventHandler('onPressStart')}
+          onPressEnd={createEventHandler('onPressEnd')}>
+          <div ref={ref} />
+        </Press>
+      );
+
+      ReactDOM.render(element, container);
+
+      ref.current.getBoundingClientRect = getBoundingClientRectMock;
+      ref.current.dispatchEvent(
+        createPointerEvent('pointerdown', {
+          pointerType: 'mouse',
+        }),
+      );
+      ref.current.dispatchEvent(
+        createPointerEvent('pointermove', {
+          ...coordinatesInside,
+          pointerType: 'mouse',
+        }),
+      );
+      container.dispatchEvent(
+        createPointerEvent('pointermove', {
+          ...coordinatesOutside,
+          pointerType: 'mouse',
+        }),
+      );
+      container.dispatchEvent(
+        createPointerEvent('pointermove', {
+          ...coordinatesInside,
+          pointerType: 'mouse',
+        }),
+      );
+      container.dispatchEvent(
+        createPointerEvent('pointerup', {
+          ...coordinatesInside,
+          pointerType: 'mouse',
+        }),
+      );
+      jest.runAllTimers();
+
+      expect(events).toEqual([
+        'onPressStart',
+        'onPressChange',
+        'onPressMove',
+        'onPressEnd',
+        'onPressChange',
+        'onPressStart',
+        'onPressChange',
+        'onPressEnd',
+        'onPressChange',
+        'onPress',
+      ]);
+    });
+
+    it('"onPress" is called on re-entry to hit rect for touch', () => {
+      let events = [];
+      const ref = React.createRef();
+      const createEventHandler = msg => () => {
+        events.push(msg);
+      };
+
+      const element = (
+        <Press
+          onPress={createEventHandler('onPress')}
+          onPressChange={createEventHandler('onPressChange')}
+          onPressMove={createEventHandler('onPressMove')}
+          onPressStart={createEventHandler('onPressStart')}
+          onPressEnd={createEventHandler('onPressEnd')}>
+          <div ref={ref} />
+        </Press>
+      );
+
+      ReactDOM.render(element, container);
+
+      ref.current.getBoundingClientRect = getBoundingClientRectMock;
+      ref.current.dispatchEvent(
+        createPointerEvent('pointerdown', {
+          pointerType: 'touch',
+        }),
+      );
+      ref.current.dispatchEvent(
+        createPointerEvent('pointermove', {
+          ...coordinatesInside,
+          pointerType: 'touch',
+        }),
+      );
+      container.dispatchEvent(
+        createPointerEvent('pointermove', {
+          ...coordinatesOutside,
+          pointerType: 'touch',
+        }),
+      );
+      container.dispatchEvent(
+        createPointerEvent('pointermove', {
+          ...coordinatesInside,
+          pointerType: 'touch',
+        }),
+      );
+      container.dispatchEvent(
+        createPointerEvent('pointerup', {
+          ...coordinatesInside,
+          pointerType: 'touch',
+        }),
+      );
+      jest.runAllTimers();
+
+      expect(events).toEqual([
+        'onPressStart',
+        'onPressChange',
+        'onPressMove',
+        'onPressEnd',
+        'onPressChange',
+        'onPressStart',
+        'onPressChange',
+        'onPressEnd',
+        'onPressChange',
+        'onPress',
+      ]);
+    });
   });
 
   describe('delayed and multiple events', () => {