diff --git a/docs/release-notes/.FSharp.Compiler.Service/11.0.100.md b/docs/release-notes/.FSharp.Compiler.Service/11.0.100.md
index 4a6110cf514..a20e7204a0d 100644
--- a/docs/release-notes/.FSharp.Compiler.Service/11.0.100.md
+++ b/docs/release-notes/.FSharp.Compiler.Service/11.0.100.md
@@ -54,6 +54,7 @@
 * Fix parallel compilation of scripts ([PR #19649](https://github.com/dotnet/fsharp/pull/19649))
 * Fix parser recovery, name resolution, and code completion for unfinished enum patterns ([PR #19708](https://github.com/dotnet/fsharp/pull/19708))
 * Parser: fix unexpected diagnostics in debug builds, improve error messages ([PR #19730](https://github.com/dotnet/fsharp/pull/19730))
+* Fix overload resolution of static member extension on generic types when the call uses explicit type arguments and an intrinsic overload of the same name exists. ([Issue #19664](https://github.com/dotnet/fsharp/issues/19664), [PR #19736](https://github.com/dotnet/fsharp/pull/19736))
 
 ### Added
 
diff --git a/src/Compiler/Checking/NameResolution.fs b/src/Compiler/Checking/NameResolution.fs
index 54290c21bd0..0650a43d300 100644
--- a/src/Compiler/Checking/NameResolution.fs
+++ b/src/Compiler/Checking/NameResolution.fs
@@ -2874,6 +2874,20 @@ let rec ResolveLongIdentInTypePrim (ncenv: NameResolver) nenv lookupKind (resInf
             | Some(MethodItem msets) when isLookUpExpr ->
                 let minfos = msets |> ExcludeHiddenOfMethInfos g ncenv.amap m
 
+                // If the intrinsic candidate set already disagrees with the strict
+                // instance/static filter (e.g. expression-form `Type<TArg>.Member` is
+                // resolved as a dot-expression with LookupIsInstance.Yes but yields
+                // static intrinsic members), relax the filter for the extension lookup
+                // so static extension members are also considered. See issue #19664.
+                let isInstanceFilter =
+                    match isInstanceFilter with
+                    | LookupIsInstance.Ambivalent -> isInstanceFilter
+                    | LookupIsInstance.Yes when minfos |> List.exists (fun m -> not m.IsInstance) ->
+                        LookupIsInstance.Ambivalent
+                    | LookupIsInstance.No when minfos |> List.exists (fun m -> m.IsInstance) ->
+                        LookupIsInstance.Ambivalent
+                    | _ -> isInstanceFilter
+
                 // fold the available extension members into the overload resolution
                 let extensionMethInfos = ExtensionMethInfosOfTypeInScope ResultCollectionSettings.AllResults ncenv.InfoReader nenv ad optFilter isInstanceFilter m ty
 
diff --git a/tests/FSharp.Compiler.ComponentTests/Conformance/BasicGrammarElements/MethodResolution/StaticMethodResolution.fs b/tests/FSharp.Compiler.ComponentTests/Conformance/BasicGrammarElements/MethodResolution/StaticMethodResolution.fs
new file mode 100644
index 00000000000..59250d79e8a
--- /dev/null
+++ b/tests/FSharp.Compiler.ComponentTests/Conformance/BasicGrammarElements/MethodResolution/StaticMethodResolution.fs
@@ -0,0 +1,42 @@
+// Copyright (c) Microsoft Corporation.  All Rights Reserved.  See License.txt in the project root for license information.
+
+namespace Conformance.BasicGrammarElements
+
+open FSharp.Test.Compiler
+open Xunit
+
+module StaticMethodResolution =
+
+    // Regression test for https://github.com/dotnet/fsharp/issues/19664
+    //
+    // When a static extension method is defined in a *different* [<AutoOpen>] module than
+    // the generic type it extends, and shares its name with an intrinsic static member,
+    // resolving the call via the explicit-type-argument syntax `Type<TArg>.Member(...)`
+    // previously failed with FS0505. The non-generic dotted form `Type.Member(...)`
+    // resolved correctly, so any regression test that omits the explicit type arguments
+    // does not actually exercise the bug. See the discussion at
+    // https://github.com/dotnet/fsharp/issues/19675#issuecomment-4373059900.
+    [<Fact>]
+    let ``Static extension on generic type resolves with explicit type arguments (issue 19664)`` () =
+        Fsx """
+module Extensions =
+
+    type StaticGeneric<'T> =
+        static member Bar() = ()
+        static member Bar(_: int, _: int) = ()
+
+    [<AutoOpen>]
+    module StaticGenericExtensions =
+        type StaticGeneric<'T> with
+            static member Bar(_: int) = ()
+
+module Program =
+    open Extensions
+
+    StaticGeneric<int>.Bar()        // intrinsic, 0 args
+    StaticGeneric<int>.Bar(42)      // regressed: extension, 1 arg, see issue 19664 (FS0505)
+    StaticGeneric<int>.Bar(42, 0)   // intrinsic, 2 args
+        """
+        |> withOptions ["--nowarn:1125"]
+        |> typecheck
+        |> shouldSucceed
diff --git a/tests/FSharp.Compiler.ComponentTests/FSharp.Compiler.ComponentTests.fsproj b/tests/FSharp.Compiler.ComponentTests/FSharp.Compiler.ComponentTests.fsproj
index 50937f9945b..bdbca65675a 100644
--- a/tests/FSharp.Compiler.ComponentTests/FSharp.Compiler.ComponentTests.fsproj
+++ b/tests/FSharp.Compiler.ComponentTests/FSharp.Compiler.ComponentTests.fsproj
@@ -65,6 +65,7 @@
     <Compile Include="Conformance\BasicGrammarElements\MemberDefinitions\OptionalDefaultParamArgs\OptionalDefaultParamArgs.fs" />
     <Compile Include="Conformance\BasicGrammarElements\MemberDefinitions\OverloadingMembers\OverloadingMembers.fs" />
     <Compile Include="Conformance\BasicGrammarElements\MethodResolution\MethodResolution.fs" />
+    <Compile Include="Conformance\BasicGrammarElements\MethodResolution\StaticMethodResolution.fs" />
     <Compile Include="Conformance\BasicGrammarElements\ModuleAbbreviations\ModuleAbbreviations.fs" />
     <Compile Include="Conformance\BasicGrammarElements\ModuleDefinitions\ModuleDefinitions.fs" />
     <Compile Include="Conformance\BasicGrammarElements\NamespaceDeclGroups\NamespaceDeclGroups.fs" />