diff --git a/Changelog.md b/Changelog.md
index 230eafa46..b4e7e6b3a 100644
--- a/Changelog.md
+++ b/Changelog.md
@@ -1,5 +1,10 @@
 ### Development
-[Full Changelog](http://github.com/rspec/rspec-expectations/compare/v3.12.3...main)
+[Full Changelog](http://github.com/rspec/rspec-expectations/compare/v3.13.0...main)
+
+Bug Fixes:
+
+* Fix the false positive warning message for negated raise error with a regexp argument.
+  (Eric Mueller, #1456)
 
 ### 3.13.0 / 2024-02-04
 [Full Changelog](http://github.com/rspec/rspec-expectations/compare/v3.12.4...v3.13.0)
diff --git a/lib/rspec/matchers/built_in/raise_error.rb b/lib/rspec/matchers/built_in/raise_error.rb
index 162fe056d..bbaaf623f 100644
--- a/lib/rspec/matchers/built_in/raise_error.rb
+++ b/lib/rspec/matchers/built_in/raise_error.rb
@@ -13,6 +13,10 @@ class RaiseError
         # argument. We can't use `nil` for that because we need to warn when `nil` is
         # passed in a different way. It's an Object, not a Module, since Module's `===`
         # does not evaluate to true when compared to itself.
+        #
+        # Note; this _is_ the default value supplied for expected_error_or_message, but
+        # because there are two method-calls involved, that default is actually supplied
+        # in the definition of the _matcher_ method, `RSpec::Matchers#raise_error`
         UndefinedValue = Object.new.freeze
 
         def initialize(expected_error_or_message, expected_message, &block)
@@ -25,7 +29,7 @@ def initialize(expected_error_or_message, expected_message, &block)
           when nil, UndefinedValue
             @expected_error = Exception
             @expected_message = expected_message
-          when String
+          when String, Regexp
             @expected_error = Exception
             @expected_message = expected_error_or_message
           else
diff --git a/spec/rspec/matchers/built_in/raise_error_spec.rb b/spec/rspec/matchers/built_in/raise_error_spec.rb
index 5fa74ffd4..f2a388fd6 100644
--- a/spec/rspec/matchers/built_in/raise_error_spec.rb
+++ b/spec/rspec/matchers/built_in/raise_error_spec.rb
@@ -290,13 +290,28 @@ def to_s
   end
 end
 
-RSpec.describe "expect { ... }.not_to raise_error(message)" do
-  it "issues a warning" do
-    expect_warning_with_call_site __FILE__, __LINE__+1, /risks false positives/
+RSpec.describe "expect { ... }.not_to raise_error('message')" do
+  it "issues a warning when configured to do so", :warn_about_potential_false_positives do
+    RSpec::Expectations.configuration.warn_about_potential_false_positives = true
+    expect_warning_with_call_site __FILE__, __LINE__+1, /not_to raise_error\(message\)` risks false positives/
+    expect { raise 'blarg' }.not_to raise_error('blah')
+  end
+
+  it "supresses the warning when configured to do so", :warn_about_potential_false_positives do
+    RSpec::Expectations.configuration.warn_about_potential_false_positives = false
+    expect_no_warnings
+    expect { raise 'blarg' }.not_to raise_error('blah')
+  end
+end
+
+RSpec.describe "expect { ... }.not_to raise_error(/message/)" do
+  it "issues a warning when configured to do so", :warn_about_potential_false_positives do
+    RSpec::Expectations.configuration.warn_about_potential_false_positives = true
+    expect_warning_with_call_site __FILE__, __LINE__+1, /not_to raise_error\(message\)` risks false positives/
     expect { raise 'blarg' }.not_to raise_error(/blah/)
   end
 
-  it "can supresses the warning when configured to do so", :warn_about_potential_false_positives do
+  it "supresses the warning when configured to do so", :warn_about_potential_false_positives do
     RSpec::Expectations.configuration.warn_about_potential_false_positives = false
     expect_no_warnings
     expect { raise 'blarg' }.not_to raise_error(/blah/)