diff --git a/native/chat/inner-text-message.react.js b/native/chat/inner-text-message.react.js
--- a/native/chat/inner-text-message.react.js
+++ b/native/chat/inner-text-message.react.js
@@ -99,6 +99,30 @@
     return [styles.text, textStyle];
   }, [darkColor]);
 
+  // If we need to render a Text with an onPress prop inside, we're going to
+  // have an issue: the GestureTouchableOpacity below will trigger too when the
+  // the onPress is pressed. We have to use a GestureTouchableOpacity in order
+  // for the message touch gesture to play nice with the message swipe gesture,
+  // so we need to find a way to disable the GestureTouchableOpacity.
+  //
+  // Our solution is to keep using the GestureTouchableOpacity for the padding
+  // around the text, and to have the Texts inside ALL implement an onPress prop
+  // that will default to the message touch gesture. Luckily, Text with onPress
+  // plays nice with the message swipe gesture.
+  let secondMessage;
+  if (textMessageMarkdown.markdownHasPressable) {
+    secondMessage = (
+      <View
+        style={[StyleSheet.absoluteFill, styles.message]}
+        pointerEvents="box-none"
+      >
+        <Markdown style={markdownStyles} rules={rules}>
+          {text}
+        </Markdown>
+      </View>
+    );
+  }
+
   const message = (
     <TextMessageMarkdownContext.Provider value={textMessageMarkdown}>
       <TouchableWithoutFeedback>
@@ -114,6 +138,7 @@
               {text}
             </Markdown>
           </GestureTouchableOpacity>
+          {secondMessage}
         </View>
       </TouchableWithoutFeedback>
     </TextMessageMarkdownContext.Provider>
diff --git a/native/markdown/markdown-paragraph.react.js b/native/markdown/markdown-paragraph.react.js
new file mode 100644
--- /dev/null
+++ b/native/markdown/markdown-paragraph.react.js
@@ -0,0 +1,29 @@
+// @flow
+
+import * as React from 'react';
+import { Text } from 'react-native';
+
+import { MessagePressResponderContext } from '../chat/message-press-responder-context';
+import type { TextStyle } from '../types/styles';
+
+type Props = {
+  +style?: ?TextStyle,
+  +children: React.Node,
+};
+function MarkdownParagraph(props: Props): React.Node {
+  const messagePressResponderContext = React.useContext(
+    MessagePressResponderContext,
+  );
+  const onPressMessage = messagePressResponderContext?.onPressMessage;
+  return (
+    <Text
+      style={props.style}
+      onPress={onPressMessage}
+      onLongPress={onPressMessage}
+    >
+      {props.children}
+    </Text>
+  );
+}
+
+export default MarkdownParagraph;
diff --git a/native/markdown/rules.react.js b/native/markdown/rules.react.js
--- a/native/markdown/rules.react.js
+++ b/native/markdown/rules.react.js
@@ -12,6 +12,7 @@
 
 import { useSelector } from '../redux/redux-utils';
 import MarkdownLink from './markdown-link.react';
+import MarkdownParagraph from './markdown-paragraph.react';
 import { getMarkdownStyles } from './styles';
 
 export type MarkdownRules = {
@@ -96,9 +97,9 @@
         output: SharedMarkdown.Output<SharedMarkdown.ReactElement>,
         state: SharedMarkdown.State,
       ) => (
-        <Text key={state.key} style={state.textStyle}>
+        <MarkdownParagraph key={state.key} style={state.textStyle}>
           {output(node.content, state)}
-        </Text>
+        </MarkdownParagraph>
       ),
     },
     // This is the leaf node in the AST returned by the parse phase