diff --git a/muted-tests.yml b/muted-tests.yml
index 64a890f5e7298..2c8a9aa2b22b9 100644
--- a/muted-tests.yml
+++ b/muted-tests.yml
@@ -407,12 +407,6 @@ tests:
 - class: org.elasticsearch.backwards.MixedClusterClientYamlTestSuiteIT
   method: test {p0=synonyms/90_synonyms_reloading_for_synset/Reload analyzers for specific synonym set}
   issue: https://github.com/elastic/elasticsearch/issues/116777
-- class: org.elasticsearch.xpack.ml.integration.InferenceIngestInputConfigIT
-  method: testIngestWithInputFields
-  issue: https://github.com/elastic/elasticsearch/issues/118092
-- class: org.elasticsearch.xpack.ml.integration.InferenceIngestInputConfigIT
-  method: testIngestWithMultipleInputFields
-  issue: https://github.com/elastic/elasticsearch/issues/118093
 - class: org.elasticsearch.search.fieldcaps.FieldCapabilitiesIT
   method: testRelocation
   issue: https://github.com/elastic/elasticsearch/issues/119280
@@ -439,18 +433,6 @@ tests:
 - class: org.elasticsearch.search.profile.dfs.DfsProfilerIT
   method: testProfileDfs
   issue: https://github.com/elastic/elasticsearch/issues/119711
-- class: org.elasticsearch.xpack.ml.integration.MlJobIT
-  method: testCreateJobInCustomSharedIndexUpdatesMapping
-  issue: https://github.com/elastic/elasticsearch/issues/119660
-- class: org.elasticsearch.xpack.ml.integration.MlJobIT
-  method: testUsage
-  issue: https://github.com/elastic/elasticsearch/issues/119659
-- class: org.elasticsearch.xpack.ml.integration.MlJobIT
-  method: testOpenJob_GivenTimeout_Returns408
-  issue: https://github.com/elastic/elasticsearch/issues/119810
-- class: org.elasticsearch.xpack.ml.integration.MlJobIT
-  method: testGetJob_GivenJobExists
-  issue: https://github.com/elastic/elasticsearch/issues/119811
 - class: org.elasticsearch.xpack.security.authc.ldap.ADLdapUserSearchSessionFactoryTests
   issue: https://github.com/elastic/elasticsearch/issues/119882
 - class: org.elasticsearch.index.mapper.AbstractShapeGeometryFieldMapperTests
diff --git a/x-pack/plugin/ml/qa/native-multi-node-tests/src/javaRestTest/java/org/elasticsearch/xpack/ml/integration/DatafeedJobsIT.java b/x-pack/plugin/ml/qa/native-multi-node-tests/src/javaRestTest/java/org/elasticsearch/xpack/ml/integration/DatafeedJobsIT.java
index 5287d149fae3d..367c1cee8b0ee 100644
--- a/x-pack/plugin/ml/qa/native-multi-node-tests/src/javaRestTest/java/org/elasticsearch/xpack/ml/integration/DatafeedJobsIT.java
+++ b/x-pack/plugin/ml/qa/native-multi-node-tests/src/javaRestTest/java/org/elasticsearch/xpack/ml/integration/DatafeedJobsIT.java
@@ -11,6 +11,8 @@
 import org.elasticsearch.ElasticsearchException;
 import org.elasticsearch.ElasticsearchStatusException;
 import org.elasticsearch.ResourceNotFoundException;
+import org.elasticsearch.action.admin.cluster.node.tasks.cancel.CancelTasksRequest;
+import org.elasticsearch.action.admin.cluster.node.tasks.cancel.TransportCancelTasksAction;
 import org.elasticsearch.action.search.SearchRequest;
 import org.elasticsearch.action.support.master.AcknowledgedResponse;
 import org.elasticsearch.common.ReferenceDocs;
@@ -80,6 +82,10 @@ public class DatafeedJobsIT extends MlNativeAutodetectIntegTestCase {
     public void cleanup() {
         updateClusterSettings(Settings.builder().putNull("logger.org.elasticsearch.xpack.ml.datafeed"));
         cleanUp();
+        // Race conditions between closing and killing tasks in these tests,
+        // sometimes result in lingering persistent tasks (such as "_close"),
+        // which cause subsequent tests to fail.
+        client().execute(TransportCancelTasksAction.TYPE, new CancelTasksRequest());
     }
 
     public void testLookbackOnly() throws Exception {