diff --git a/CHANGES b/CHANGES
index ed864de051..12d5d8f3da 100644
--- a/CHANGES
+++ b/CHANGES
@@ -33,6 +33,8 @@ Bugs fixed
 * #6564: html: a width of table was ignored on HTML builder
 * #7401: Incorrect argument is passed for :event:`env-get-outdated` handlers
 * #7355: autodoc: a signature of cython-function is not recognized well
+* #7409: intersphinx: ValueError is raised when an extension sets up
+  :confval:`intersphinx_mapping` on :event:`config-inited` event
 
 Testing
 --------
diff --git a/sphinx/builders/epub3.py b/sphinx/builders/epub3.py
index 5d7121fe6d..cf795f3baf 100644
--- a/sphinx/builders/epub3.py
+++ b/sphinx/builders/epub3.py
@@ -282,7 +282,7 @@ def setup(app: Sphinx) -> Dict[str, Any]:
                          ENUM('horizontal', 'vertical'))
 
     # event handlers
-    app.connect('config-inited', convert_epub_css_files)
+    app.connect('config-inited', convert_epub_css_files, priority=800)
     app.connect('builder-inited', validate_config_values)
 
     return {
diff --git a/sphinx/builders/html/__init__.py b/sphinx/builders/html/__init__.py
index 6488146d57..320c7feb6b 100644
--- a/sphinx/builders/html/__init__.py
+++ b/sphinx/builders/html/__init__.py
@@ -1231,12 +1231,12 @@ def setup(app: Sphinx) -> Dict[str, Any]:
     app.add_config_value('html4_writer', False, 'html')
 
     # event handlers
-    app.connect('config-inited', convert_html_css_files)
-    app.connect('config-inited', convert_html_js_files)
-    app.connect('config-inited', validate_html_extra_path)
-    app.connect('config-inited', validate_html_static_path)
-    app.connect('config-inited', validate_html_logo)
-    app.connect('config-inited', validate_html_favicon)
+    app.connect('config-inited', convert_html_css_files, priority=800)
+    app.connect('config-inited', convert_html_js_files, priority=800)
+    app.connect('config-inited', validate_html_extra_path, priority=800)
+    app.connect('config-inited', validate_html_static_path, priority=800)
+    app.connect('config-inited', validate_html_logo, priority=800)
+    app.connect('config-inited', validate_html_favicon, priority=800)
     app.connect('builder-inited', validate_math_renderer)
     app.connect('html-page-context', setup_js_tag_helper)
 
diff --git a/sphinx/builders/latex/__init__.py b/sphinx/builders/latex/__init__.py
index 1348f0e125..390a5d9c7b 100644
--- a/sphinx/builders/latex/__init__.py
+++ b/sphinx/builders/latex/__init__.py
@@ -536,7 +536,7 @@ def setup(app: Sphinx) -> Dict[str, Any]:
     app.setup_extension('sphinx.builders.latex.transforms')
 
     app.add_builder(LaTeXBuilder)
-    app.connect('config-inited', validate_config_values)
+    app.connect('config-inited', validate_config_values, priority=800)
 
     app.add_config_value('latex_engine', default_latex_engine, None,
                          ENUM('pdflatex', 'xelatex', 'lualatex', 'platex', 'uplatex'))
diff --git a/sphinx/config.py b/sphinx/config.py
index 87007c33d0..19a8f6c4f5 100644
--- a/sphinx/config.py
+++ b/sphinx/config.py
@@ -478,11 +478,11 @@ def check_master_doc(app: "Sphinx", env: "BuildEnvironment", added: Set[str],
 
 
 def setup(app: "Sphinx") -> Dict[str, Any]:
-    app.connect('config-inited', convert_source_suffix)
-    app.connect('config-inited', init_numfig_format)
-    app.connect('config-inited', correct_copyright_year)
-    app.connect('config-inited', check_confval_types)
-    app.connect('config-inited', check_primary_domain)
+    app.connect('config-inited', convert_source_suffix, priority=800)
+    app.connect('config-inited', init_numfig_format, priority=800)
+    app.connect('config-inited', correct_copyright_year, priority=800)
+    app.connect('config-inited', check_confval_types, priority=800)
+    app.connect('config-inited', check_primary_domain, priority=800)
     app.connect('env-get-outdated', check_master_doc)
 
     return {
diff --git a/sphinx/ext/intersphinx.py b/sphinx/ext/intersphinx.py
index 5aa9c75f0f..02f605bacf 100644
--- a/sphinx/ext/intersphinx.py
+++ b/sphinx/ext/intersphinx.py
@@ -367,7 +367,7 @@ def setup(app: Sphinx) -> Dict[str, Any]:
     app.add_config_value('intersphinx_mapping', {}, True)
     app.add_config_value('intersphinx_cache_limit', 5, False)
     app.add_config_value('intersphinx_timeout', None, False)
-    app.connect('config-inited', normalize_intersphinx_mapping)
+    app.connect('config-inited', normalize_intersphinx_mapping, priority=800)
     app.connect('builder-inited', load_mappings)
     app.connect('missing-reference', missing_reference)
     return {
diff --git a/sphinx/extension.py b/sphinx/extension.py
index 45ea46677d..fa7a0d490c 100644
--- a/sphinx/extension.py
+++ b/sphinx/extension.py
@@ -60,7 +60,7 @@ def verify_needs_extensions(app: "Sphinx", config: Config) -> None:
 
 
 def setup(app: "Sphinx") -> Dict[str, Any]:
-    app.connect('config-inited', verify_needs_extensions)
+    app.connect('config-inited', verify_needs_extensions, priority=800)
 
     return {
         'version': 'builtin',
diff --git a/sphinx/registry.py b/sphinx/registry.py
index 93a7ebc253..200f59d422 100644
--- a/sphinx/registry.py
+++ b/sphinx/registry.py
@@ -453,7 +453,7 @@ def merge_source_suffix(app: "Sphinx", config: Config) -> None:
 
 
 def setup(app: "Sphinx") -> Dict[str, Any]:
-    app.connect('config-inited', merge_source_suffix)
+    app.connect('config-inited', merge_source_suffix, priority=800)
 
     return {
         'version': 'builtin',