diff --git a/moto/kms/utils.py b/moto/kms/utils.py
index 89898d032..8d53051c2 100644
--- a/moto/kms/utils.py
+++ b/moto/kms/utils.py
@@ -190,12 +190,17 @@ class RSAPrivateKey(AbstractPrivateKey):
             pad = padding.PSS(
                 mgf=padding.MGF1(hashes.SHA256()), salt_length=padding.PSS.MAX_LENGTH
             )
-            algorithm = hashes.SHA256()
+            algorithm = hashes.SHA256()  # type: Any
+        elif signing_algorithm == SigningAlgorithm.RSASSA_PSS_SHA_384:
+            pad = padding.PSS(
+                mgf=padding.MGF1(hashes.SHA384()), salt_length=padding.PSS.MAX_LENGTH
+            )
+            algorithm = hashes.SHA384()
         else:
             pad = padding.PSS(
-                mgf=padding.MGF1(hashes.SHA256()), salt_length=padding.PSS.MAX_LENGTH
+                mgf=padding.MGF1(hashes.SHA512()), salt_length=padding.PSS.MAX_LENGTH
             )
-            algorithm = hashes.SHA256()
+            algorithm = hashes.SHA512()
         return self.private_key.sign(message, pad, algorithm)
 
     def verify(self, message: bytes, signature: bytes, signing_algorithm: str) -> bool:
@@ -207,12 +212,17 @@ class RSAPrivateKey(AbstractPrivateKey):
             pad = padding.PSS(
                 mgf=padding.MGF1(hashes.SHA256()), salt_length=padding.PSS.MAX_LENGTH
             )
-            algorithm = hashes.SHA256()
+            algorithm = hashes.SHA256()  # type: Any
+        elif signing_algorithm == SigningAlgorithm.RSASSA_PSS_SHA_384:
+            pad = padding.PSS(
+                mgf=padding.MGF1(hashes.SHA384()), salt_length=padding.PSS.MAX_LENGTH
+            )
+            algorithm = hashes.SHA384()
         else:
             pad = padding.PSS(
-                mgf=padding.MGF1(hashes.SHA256()), salt_length=padding.PSS.MAX_LENGTH
+                mgf=padding.MGF1(hashes.SHA512()), salt_length=padding.PSS.MAX_LENGTH
             )
-            algorithm = hashes.SHA256()
+            algorithm = hashes.SHA512()
 
         public_key = self.private_key.public_key()
         try:
diff --git a/tests/test_kms/test_kms_boto3.py b/tests/test_kms/test_kms_boto3.py
index 3895df617..ca2b75241 100644
--- a/tests/test_kms/test_kms_boto3.py
+++ b/tests/test_kms/test_kms_boto3.py
@@ -2,11 +2,13 @@ import json
 from datetime import datetime
 from cryptography.hazmat.primitives import hashes
 from cryptography.hazmat.primitives.asymmetric import rsa
+import itertools
 from unittest import mock
 from dateutil.tz import tzutc
 import base64
 import os
 
+
 import boto3
 import botocore.exceptions
 from botocore.exceptions import ClientError
@@ -1163,8 +1165,16 @@ def test_sign_and_verify_ignoring_grant_tokens():
 
 
 @mock_kms
-@pytest.mark.parametrize("key_spec", ["RSA_2048", "RSA_3072", "RSA_4096"])
-def test_sign_and_verify_digest_message_type_RSASSA_PSS_SHA_256(key_spec):
+@pytest.mark.parametrize(
+    "key_spec, signing_algorithm",
+    list(
+        itertools.product(
+            ["RSA_2048", "RSA_3072", "RSA_4096"],
+            ["RSASSA_PSS_SHA_256", "RSASSA_PSS_SHA_384", "RSASSA_PSS_SHA_512"],
+        )
+    ),
+)
+def test_sign_and_verify_digest_message_type_RSA(key_spec, signing_algorithm):
     client = boto3.client("kms", region_name="us-west-2")
 
     key = client.create_key(
@@ -1176,7 +1186,6 @@ def test_sign_and_verify_digest_message_type_RSASSA_PSS_SHA_256(key_spec):
     digest.update(b"this works")
     digest.update(b"as well")
     message = digest.finalize()
-    signing_algorithm = "RSASSA_PSS_SHA_256"
 
     sign_response = client.sign(
         KeyId=key_id,