diff --git a/src/app/mod.rs b/src/app/mod.rs
index 59085c58..3fd4ad66 100644
--- a/src/app/mod.rs
+++ b/src/app/mod.rs
@@ -745,7 +745,7 @@ impl<App: Application> ApplicationExt for App {
 
         // Show any current dialog on top and centered over the view content
         // We have to use a popover even without a dialog to keep the tree from changing
-        let mut popover = popover(view_column);
+        let mut popover = popover(view_column).modal(true);
         if let Some(dialog) = self.dialog() {
             popover = popover.popup(dialog.map(Message::App));
         }
diff --git a/src/widget/popover.rs b/src/widget/popover.rs
index 2136ba9a..1d9055ad 100644
--- a/src/widget/popover.rs
+++ b/src/widget/popover.rs
@@ -34,6 +34,7 @@ pub enum Position {
 #[must_use]
 pub struct Popover<'a, Message, Renderer> {
     content: Element<'a, Message, crate::Theme, Renderer>,
+    modal: bool,
     // XXX Avoid refcell; improve iced overlay API?
     popup: Option<RefCell<Element<'a, Message, crate::Theme, Renderer>>>,
     position: Position,
@@ -43,11 +44,18 @@ impl<'a, Message, Renderer> Popover<'a, Message, Renderer> {
     pub fn new(content: impl Into<Element<'a, Message, crate::Theme, Renderer>>) -> Self {
         Self {
             content: content.into(),
+            modal: false,
             popup: None,
             position: Position::Center,
         }
     }
 
+    /// A modal popup interrupts user inputs and demands action.
+    pub fn modal(mut self, modal: bool) -> Self {
+        self.modal = modal;
+        self
+    }
+
     pub fn popup(mut self, popup: impl Into<Element<'a, Message, crate::Theme, Renderer>>) -> Self {
         self.popup = Some(RefCell::new(popup.into()));
         self
@@ -127,11 +135,13 @@ where
         shell: &mut Shell<'_, Message>,
         viewport: &Rectangle,
     ) -> event::Status {
-        if matches!(
-            event,
-            Event::Mouse(mouse::Event::ButtonPressed(_))
-                | Event::Touch(touch::Event::FingerPressed { .. })
-        ) {
+        if !self.modal
+            && matches!(
+                event,
+                Event::Mouse(mouse::Event::ButtonPressed(_))
+                    | Event::Touch(touch::Event::FingerPressed { .. })
+            )
+        {
             let state = tree.state.downcast_mut::<State>();
             state.is_open = cursor_position.is_over(layout.bounds());
         }