diff --git a/compose/ui/ui/src/uikitMain/kotlin/androidx/compose/ui/window/UserInputView.uikit.kt b/compose/ui/ui/src/uikitMain/kotlin/androidx/compose/ui/window/UserInputView.uikit.kt
index 3c92c3f58645c..ae32a28b93438 100644
--- a/compose/ui/ui/src/uikitMain/kotlin/androidx/compose/ui/window/UserInputView.uikit.kt
+++ b/compose/ui/ui/src/uikitMain/kotlin/androidx/compose/ui/window/UserInputView.uikit.kt
@@ -37,6 +37,8 @@ import platform.CoreGraphics.CGPointMake
 import platform.CoreGraphics.CGRectZero
 import platform.UIKit.UIEvent
 import platform.UIKit.UIGestureRecognizer
+import platform.UIKit.UITapGestureRecognizer
+import platform.UIKit.UIScreenEdgePanGestureRecognizer
 import platform.UIKit.UIGestureRecognizerDelegateProtocol
 import platform.UIKit.UIGestureRecognizerState
 import platform.UIKit.UIGestureRecognizerStateBegan
@@ -135,13 +137,19 @@ private class UserInputGestureRecognizerDelegateProxy : CMPGestureRecognizerDele
     ): Boolean {
         // We should recognize simultaneously only with the gesture recognizers
         // belonging to itself or to the views up in the hierarchy.
+        // An exception: UIScreenEdgePanGestureRecognizer, this always has precedence over us and is
+        // not allowed to recognize simultaneously
 
-        // Can't check if either view is null
+        // Can't proceed if either view is null
         val view = gestureRecognizer.view ?: return false
         val otherView = otherGestureRecognizer.view ?: return false
 
         val otherIsAscendant = !otherView.isDescendantOfView(view)
 
+        if (otherIsAscendant && otherGestureRecognizer is UIScreenEdgePanGestureRecognizer) {
+            return false
+        }
+
         // Only allow simultaneous recognition if the other gesture recognizer is attached to the same view
         // or to a view up in the hierarchy
         return otherView == view || otherIsAscendant
@@ -151,10 +159,30 @@ private class UserInputGestureRecognizerDelegateProxy : CMPGestureRecognizerDele
         gestureRecognizer: UIGestureRecognizer,
         otherGestureRecognizer: UIGestureRecognizer
     ): Boolean {
-        // We don't require other gesture recognizers to fail.
-        // Assumption is that we recognize
-        // simultaneously with the gesture recognizers of the views up in the hierarchy.
-        // And gesture recognizers down the hierarchy require to failure us.
+        // Two situations are possible here.
+        // 1. If it's a gesture recognizer of a descendant (interop) view,
+        // we should wait until it fails,
+        // if it's a UITapGestureRecognizer.
+        //
+        // 2. It's a gesture recognizer of the view itself, or it's an ascendant view.
+        // We don't require failure of it, unless it's a `UIScreenEdgePanGestureRecognizer`.
+
+        val view = gestureRecognizer.view ?: return false
+        val otherView = otherGestureRecognizer.view ?: return false
+
+        val otherIsDescendant = otherView.isDescendantOfView(view)
+        val otherIsAscendantOrSameView = !otherIsDescendant
+
+        // (1)
+        if (otherIsDescendant && otherGestureRecognizer is UITapGestureRecognizer) {
+            return true
+        }
+
+        // (2)
+        if (otherIsAscendantOrSameView && otherGestureRecognizer is UIScreenEdgePanGestureRecognizer) {
+            return true
+        }
+
         return false
     }
 
@@ -162,13 +190,24 @@ private class UserInputGestureRecognizerDelegateProxy : CMPGestureRecognizerDele
         gestureRecognizer: UIGestureRecognizer,
         otherGestureRecognizer: UIGestureRecognizer
     ): Boolean {
-        // Other gesture recognizers,
-        // except the case where it belongs to the same view,
-        // are required to wait until we fail.
-        // In practice, it can only happen when other gesture recognizers are attached to the
-        // descendant views (aka interop views).
-        // In other cases, it's allowed to recognize simultaneously, so this method will not be
-        // called
+
+        // otherGestureRecognizer is UITapGestureRecognizer,
+        // it must not wait till we fail and has priority
+        if (otherGestureRecognizer is UITapGestureRecognizer) {
+            return false
+        }
+
+        val view = gestureRecognizer.view ?: return false
+        val otherView = otherGestureRecognizer.view ?: return false
+
+        val otherIsDescendant = otherView.isDescendantOfView(view)
+        val otherIsAscendantOrSameView = !otherIsDescendant
+
+        if (otherIsAscendantOrSameView && otherGestureRecognizer is UIScreenEdgePanGestureRecognizer) {
+            return false
+        }
+
+        // Otherwise it is required to fail (aka other kind of gesture recognizer on interop view)
         return gestureRecognizer.view != otherGestureRecognizer.view
     }
 }