diff --git a/eng/Version.Details.xml b/eng/Version.Details.xml
index 4918e4fe37ac..0668c30f8208 100644
--- a/eng/Version.Details.xml
+++ b/eng/Version.Details.xml
@@ -73,18 +73,18 @@
       <Sha>6755ffefdb9899c08738941d7498d880bc25e52d</Sha>
       <SourceBuild RepoName="emsdk" ManagedOnly="true" />
     </Dependency>
-    <Dependency Name="Microsoft.Build" Version="17.13.0-preview-24568-05">
+    <Dependency Name="Microsoft.Build" Version="17.13.0-preview-24604-04">
       <Uri>https://github.com/dotnet/msbuild</Uri>
-      <Sha>37fc8280dd8516257e7d04b9fc5e426de33091f2</Sha>
+      <Sha>5491064fe8d18c8f73d8b6048d277c3ec8b81d31</Sha>
     </Dependency>
-    <Dependency Name="Microsoft.Build.Localization" Version="17.13.0-preview-24568-05">
+    <Dependency Name="Microsoft.Build.Localization" Version="17.13.0-preview-24604-04">
       <Uri>https://github.com/dotnet/msbuild</Uri>
-      <Sha>37fc8280dd8516257e7d04b9fc5e426de33091f2</Sha>
+      <Sha>5491064fe8d18c8f73d8b6048d277c3ec8b81d31</Sha>
     </Dependency>
     <!-- Intermediate is necessary for source build. -->
-    <Dependency Name="Microsoft.SourceBuild.Intermediate.msbuild" Version="17.13.0-preview-24568-05">
+    <Dependency Name="Microsoft.SourceBuild.Intermediate.msbuild" Version="17.13.0-preview-24604-04">
       <Uri>https://github.com/dotnet/msbuild</Uri>
-      <Sha>37fc8280dd8516257e7d04b9fc5e426de33091f2</Sha>
+      <Sha>5491064fe8d18c8f73d8b6048d277c3ec8b81d31</Sha>
       <SourceBuild RepoName="msbuild" ManagedOnly="true" />
     </Dependency>
     <Dependency Name="Microsoft.FSharp.Compiler" Version="13.9.200-beta.24578.1">
diff --git a/eng/Versions.props b/eng/Versions.props
index 124f4811247c..76d3deeebdd6 100644
--- a/eng/Versions.props
+++ b/eng/Versions.props
@@ -199,8 +199,8 @@
          then use that in Directory.Packages.props.
 
          At usage sites, either we use MicrosoftBuildMinimumVersion, or MicrosoftBuildVersion in source-only modes. -->
-    <MicrosoftBuildVersion>17.13.0-preview-24568-05</MicrosoftBuildVersion>
-    <MicrosoftBuildLocalizationVersion>17.13.0-preview-24568-05</MicrosoftBuildLocalizationVersion>
+    <MicrosoftBuildVersion>17.13.0-preview-24604-04</MicrosoftBuildVersion>
+    <MicrosoftBuildLocalizationVersion>17.13.0-preview-24604-04</MicrosoftBuildLocalizationVersion>
     <MicrosoftBuildMinimumVersion Condition="Exists('$(RepoRoot)src\Layout\redist\minimumMSBuildVersion') and '$(DotNetBuildSourceOnly)' != 'true'">$([System.IO.File]::ReadAllText('$(RepoRoot)src\Layout\redist\minimumMSBuildVersion').Trim())</MicrosoftBuildMinimumVersion>
   </PropertyGroup>
   <PropertyGroup>
diff --git a/test/Microsoft.NET.Build.Tests/GivenThatWeWantMSBuildToRespectCustomCulture.cs b/test/Microsoft.NET.Build.Tests/GivenThatWeWantMSBuildToRespectCustomCulture.cs
index e81667d635bc..e1697e144e6f 100644
--- a/test/Microsoft.NET.Build.Tests/GivenThatWeWantMSBuildToRespectCustomCulture.cs
+++ b/test/Microsoft.NET.Build.Tests/GivenThatWeWantMSBuildToRespectCustomCulture.cs
@@ -27,9 +27,32 @@ public void SupportRespectAlreadyAssignedItemCulture_ByDefault_ForDotnet9(string
             new FileInfo(Path.Combine(outputDirectory, "test-2", "MSBuildCultureResourceGeneration.resources.dll")).Should().Exist();
         }
 
-        [Theory]
         [InlineData("net7.0")]
         [InlineData("net6.0")]
+        [CoreMSBuildOnlyTheory]
+        public void SupportRespectAlreadyAssignedItemCulture_IsNotSupported_BuildShouldWarn(string targetFramework)
+        {
+            var testAsset = _testAssetsManager
+                .CopyTestAsset("MSBuildCultureResourceGeneration", identifier: targetFramework)
+                .WithSource()
+                .WithTargetFramework(targetFramework);
+
+            var buildCommand = new BuildCommand(testAsset);
+            // Custom culture is allowed, but if set explicitly and overwritten - a warning is issued.
+            buildCommand.Execute().Should().Pass().And
+                // warning MSB3002: Explicitly set culture "test-1" for item "Resources.test-1.resx" was overwritten with inferred culture "", because 'RespectAlreadyAssignedItemCulture' property was not set.
+                .HaveStdOutContaining("warning MSB3002:");
+        }
+
+        [InlineData("net7.0")]
+        [InlineData("net6.0")]
+        [FullMSBuildOnlyTheory]
+        // Is this Failing? Is full FW MSBuild already on 17.13? Then remove this test and remove `[CoreMSBuildOnlyTheory]` attribute on the test above
+        //
+        // Until MSBuild 17.13 is merged into FullFW MSBuild in sdk tests - the test will fail, as
+        //  proper recognition of custom cultures in RAR is not supported and hence the build will fail during copy:
+        //
+        // Microsoft.Common.CurrentVersion.targets(4959,5): error MSB3030: Could not copy the file "obj\Debug\net7.0\test-1\MSBuildCultureResourceGeneration.resources.dll" because it was not found.
         public void SupportRespectAlreadyAssignedItemCulture_IsNotSupported_BuildShouldFail(string targetFramework)
         {
             var testAsset = _testAssetsManager