diff --git a/compiler/testData/javaModules/noDependencyOnNamed/lib/foo/Foo.java b/compiler/testData/javaModules/noDependencyOnNamed/lib/foo/Foo.java
new file mode 100644
index 00000000000..26688f00945
--- /dev/null
+++ b/compiler/testData/javaModules/noDependencyOnNamed/lib/foo/Foo.java
@@ -0,0 +1,6 @@
+package foo;
+
+public class Foo {
+    public int field = 42;
+    public void method() {}
+}
diff --git a/compiler/testData/javaModules/noDependencyOnNamed/lib/module-info.java b/compiler/testData/javaModules/noDependencyOnNamed/lib/module-info.java
new file mode 100644
index 00000000000..1d982df087c
--- /dev/null
+++ b/compiler/testData/javaModules/noDependencyOnNamed/lib/module-info.java
@@ -0,0 +1,3 @@
+module lib {
+    exports foo;
+}
diff --git a/compiler/testData/javaModules/noDependencyOnNamed/main.txt b/compiler/testData/javaModules/noDependencyOnNamed/main.txt
new file mode 100644
index 00000000000..38772b215d4
--- /dev/null
+++ b/compiler/testData/javaModules/noDependencyOnNamed/main.txt
@@ -0,0 +1,13 @@
+compiler/testData/javaModules/noDependencyOnNamed/main/usage.kt:3:15: error: symbol is declared in module 'lib' which current module does not depend on
+fun test(foo: Foo) {
+              ^^^
+compiler/testData/javaModules/noDependencyOnNamed/main/usage.kt:4:9: error: symbol is declared in module 'lib' which current module does not depend on
+    foo.field
+        ^^^^^
+compiler/testData/javaModules/noDependencyOnNamed/main/usage.kt:5:9: error: symbol is declared in module 'lib' which current module does not depend on
+    foo.method()
+        ^^^^^^
+compiler/testData/javaModules/noDependencyOnNamed/main/usage.kt:6:5: error: symbol is declared in module 'lib' which current module does not depend on
+    Foo()
+    ^^^
+COMPILATION_ERROR
diff --git a/compiler/testData/javaModules/noDependencyOnNamed/main/module-info.java b/compiler/testData/javaModules/noDependencyOnNamed/main/module-info.java
new file mode 100644
index 00000000000..e7e86dd9f44
--- /dev/null
+++ b/compiler/testData/javaModules/noDependencyOnNamed/main/module-info.java
@@ -0,0 +1,3 @@
+module main {
+    requires kotlin.stdlib;
+}
diff --git a/compiler/testData/javaModules/noDependencyOnNamed/main/usage.kt b/compiler/testData/javaModules/noDependencyOnNamed/main/usage.kt
new file mode 100644
index 00000000000..240c80c56b0
--- /dev/null
+++ b/compiler/testData/javaModules/noDependencyOnNamed/main/usage.kt
@@ -0,0 +1,7 @@
+import foo.*
+
+fun test(foo: Foo) {
+    foo.field
+    foo.method()
+    Foo()
+}
diff --git a/compiler/testData/javaModules/noDependencyOnUnnamed/lib/foo/Foo.java b/compiler/testData/javaModules/noDependencyOnUnnamed/lib/foo/Foo.java
new file mode 100644
index 00000000000..26688f00945
--- /dev/null
+++ b/compiler/testData/javaModules/noDependencyOnUnnamed/lib/foo/Foo.java
@@ -0,0 +1,6 @@
+package foo;
+
+public class Foo {
+    public int field = 42;
+    public void method() {}
+}
diff --git a/compiler/testData/javaModules/noDependencyOnUnnamed/main.txt b/compiler/testData/javaModules/noDependencyOnUnnamed/main.txt
new file mode 100644
index 00000000000..ebb1f4250b6
--- /dev/null
+++ b/compiler/testData/javaModules/noDependencyOnUnnamed/main.txt
@@ -0,0 +1,13 @@
+compiler/testData/javaModules/noDependencyOnUnnamed/main/usage.kt:3:15: error: symbol is declared in unnamed module which is not read by current module
+fun test(foo: Foo) {
+              ^^^
+compiler/testData/javaModules/noDependencyOnUnnamed/main/usage.kt:4:9: error: symbol is declared in unnamed module which is not read by current module
+    foo.field
+        ^^^^^
+compiler/testData/javaModules/noDependencyOnUnnamed/main/usage.kt:5:9: error: symbol is declared in unnamed module which is not read by current module
+    foo.method()
+        ^^^^^^
+compiler/testData/javaModules/noDependencyOnUnnamed/main/usage.kt:6:5: error: symbol is declared in unnamed module which is not read by current module
+    Foo()
+    ^^^
+COMPILATION_ERROR
diff --git a/compiler/testData/javaModules/noDependencyOnUnnamed/main/module-info.java b/compiler/testData/javaModules/noDependencyOnUnnamed/main/module-info.java
new file mode 100644
index 00000000000..e7e86dd9f44
--- /dev/null
+++ b/compiler/testData/javaModules/noDependencyOnUnnamed/main/module-info.java
@@ -0,0 +1,3 @@
+module main {
+    requires kotlin.stdlib;
+}
diff --git a/compiler/testData/javaModules/noDependencyOnUnnamed/main/usage.kt b/compiler/testData/javaModules/noDependencyOnUnnamed/main/usage.kt
new file mode 100644
index 00000000000..240c80c56b0
--- /dev/null
+++ b/compiler/testData/javaModules/noDependencyOnUnnamed/main/usage.kt
@@ -0,0 +1,7 @@
+import foo.*
+
+fun test(foo: Foo) {
+    foo.field
+    foo.method()
+    Foo()
+}
diff --git a/compiler/tests/org/jetbrains/kotlin/jvm/modules/AbstractJavaModulesIntegrationTest.kt b/compiler/tests/org/jetbrains/kotlin/jvm/modules/AbstractJavaModulesIntegrationTest.kt
index 0c33ea1f49f..cd54e9fb4c9 100644
--- a/compiler/tests/org/jetbrains/kotlin/jvm/modules/AbstractJavaModulesIntegrationTest.kt
+++ b/compiler/tests/org/jetbrains/kotlin/jvm/modules/AbstractJavaModulesIntegrationTest.kt
@@ -35,6 +35,7 @@ abstract class AbstractJavaModulesIntegrationTest(
         addModules: List<String> = emptyList(),
         additionalKotlinArguments: List<String> = emptyList(),
         manifest: Manifest? = null,
+        destination: File? = null,
         checkKotlinOutput: (String) -> Unit = this.checkKotlinOutput(name),
     ): File {
         val paths = (modulePath + ForTestCompileRuntime.runtimeJarForTests()).joinToString(separator = File.pathSeparator) { it.path }
@@ -51,7 +52,8 @@ abstract class AbstractJavaModulesIntegrationTest(
 
         return compileLibrary(
             name,
-            additionalOptions = kotlinOptions,
+            destination ?: File(tmpdir, "$name.jar"),
+            kotlinOptions,
             compileJava = { _, javaFiles, outputDir ->
                 val javaOptions = mutableListOf(
                     "-d", outputDir.path,
@@ -63,8 +65,8 @@ abstract class AbstractJavaModulesIntegrationTest(
                 }
                 KotlinTestUtils.compileJavaFilesExternallyWithJava11(javaFiles, javaOptions)
             },
-            checkKotlinOutput = checkKotlinOutput,
-            manifest = manifest
+            checkKotlinOutput,
+            manifest
         )
     }
 
@@ -349,4 +351,27 @@ abstract class AbstractJavaModulesIntegrationTest(
             assertTrue(it, it.trimEnd().endsWith("COMPILATION_ERROR"))
         })
     }
+
+    // TODO (KT-60797): missing JAVA_MODULE_DOES_NOT_DEPEND_ON_MODULE.
+    fun testNoDependencyOnNamed() = muteForK2 {
+        // This is a test on the JAVA_MODULE_DOES_NOT_DEPEND_ON_MODULE diagnostic.
+        val lib = module("lib")
+        module("main", listOf(lib), listOf("lib"))
+    }
+
+    // TODO (KT-60797): missing JAVA_MODULE_DOES_NOT_READ_UNNAMED_MODULE.
+    fun testNoDependencyOnUnnamed() = muteForK2 {
+        // This is a test on the JAVA_MODULE_DOES_NOT_READ_UNNAMED_MODULE diagnostic.
+        // Most of the other tests in this class are compiling modules to jars, however here we need to compile the module to a directory.
+        // The reason is twofold:
+        // 1) Currently the compiler adds all classpath entries as module path entries as long as we're compiling a named module (i.e. have
+        //    `module-info.java` in the sources), see `configureSourceRoots` in `KotlinToJVMBytecodeCompiler.kt`. This is most likely
+        //    incorrect.
+        // 2) All jars found in the module path which are NOT named modules are loaded as automatic modules, see
+        //    `ClasspathRootsResolver.modularBinaryRoot`. Combined with p.1, it means that _any_ jar in the dependencies will be loaded
+        //    as either a named or an automatic module; there's no way to observe a jar that is a part of the unnamed module.
+        // In this test we're checking the diagnostic about using symbols from unnamed modules, so we need to compile 'lib' to a directory.
+        val lib = module("lib", destination = File(tmpdir, name))
+        module("main", additionalKotlinArguments = listOf("-classpath", lib.path))
+    }
 }