diff --git a/Dockerfile.test.cpu b/Dockerfile.test.cpu
index ca7352b7e7..ffa8854f5c 100644
--- a/Dockerfile.test.cpu
+++ b/Dockerfile.test.cpu
@@ -145,21 +145,20 @@ RUN if [[ ${MPI_KIND} != "None" ]]; then \
     fi
 
 # Install TensorFlow and Keras (releases).
-# Pin h5py only for tensorflow<2.5: https://github.com/h5py/h5py/issues/1732
 # Pin scipy!=1.4.0: https://github.com/scipy/scipy/issues/11237
 RUN if [[ ${TENSORFLOW_PACKAGE} != "tf-nightly" ]]; then \
         pip install --no-cache-dir ${TENSORFLOW_PACKAGE}; \
         if [[ ${KERAS_PACKAGE} != "None" ]]; then \
-            if [[ ${TENSORFLOW_PACKAGE} == tensorflow*==1.* ]] || [[ ${TENSORFLOW_PACKAGE} == tensorflow*==2.[012345].* ]]; then \
-                h5py="h5py<3"; \
-            fi; \
             pip uninstall -y keras-nightly; \
-            pip install --no-cache-dir ${KERAS_PACKAGE} ${h5py:-} "scipy!=1.4.0" "pandas<1.1.0"; \
+            pip install --no-cache-dir ${KERAS_PACKAGE} "scipy!=1.4.0" "pandas<1.1.0"; \
         fi; \
         mkdir -p ~/.keras; \
         python -c "import tensorflow as tf; tf.keras.datasets.mnist.load_data()"; \
     fi
 
+# Pin h5py < 3 for tensorflow: https://github.com/tensorflow/tensorflow/issues/44467
+RUN pip install 'h5py<3.0' --force-reinstall
+
 # Install PyTorch (releases).
 # Pin Pillow<7.0 for torchvision < 0.5.0: https://github.com/pytorch/vision/issues/1718
 # Pin Pillow!=8.3.0 for torchvision: https://github.com/pytorch/vision/issues/4146
diff --git a/Dockerfile.test.gpu b/Dockerfile.test.gpu
index afe64e1b01..e42c55c71b 100644
--- a/Dockerfile.test.gpu
+++ b/Dockerfile.test.gpu
@@ -113,16 +113,12 @@ RUN if [[ ${MPI_KIND} != "None" ]]; then \
     fi
 
 # Install TensorFlow and Keras (releases).
-# Pin h5py only for tensorflow<2.5: https://github.com/h5py/h5py/issues/1732
 # Pin scipy!=1.4.0: https://github.com/scipy/scipy/issues/11237
 RUN if [[ ${TENSORFLOW_PACKAGE} != "tf-nightly-gpu" ]]; then \
         pip install --no-cache-dir ${TENSORFLOW_PACKAGE}; \
         if [[ ${KERAS_PACKAGE} != "None" ]]; then \
-            if [[ ${TENSORFLOW_PACKAGE} == tensorflow*==1.* ]] || [[ ${TENSORFLOW_PACKAGE} == tensorflow*==2.[012345].* ]]; then \
-                h5py="h5py<3"; \
-            fi; \
             pip uninstall -y keras-nightly; \
-            pip install --no-cache-dir ${KERAS_PACKAGE} ${h5py:-} "scipy!=1.4.0" "pandas<1.1.0"; \
+            pip install --no-cache-dir ${KERAS_PACKAGE} "scipy!=1.4.0" "pandas<1.1.0"; \
         fi; \
         mkdir -p ~/.keras; \
         ldconfig /usr/local/cuda/targets/x86_64-linux/lib/stubs; \
@@ -130,6 +126,9 @@ RUN if [[ ${TENSORFLOW_PACKAGE} != "tf-nightly-gpu" ]]; then \
         ldconfig; \
     fi
 
+# Pin h5py < 3 for tensorflow: https://github.com/tensorflow/tensorflow/issues/44467
+RUN pip install 'h5py<3.0' --force-reinstall
+
 # Install PyTorch (releases).
 # Pin Pillow<7.0 for torchvision < 0.5.0: https://github.com/pytorch/vision/issues/1718
 # Pin Pillow!=8.3.0 for torchvision: https://github.com/pytorch/vision/issues/4146
diff --git a/horovod/spark/keras/tensorflow.py b/horovod/spark/keras/tensorflow.py
index 2f63724e5f..141d228ccb 100644
--- a/horovod/spark/keras/tensorflow.py
+++ b/horovod/spark/keras/tensorflow.py
@@ -19,7 +19,7 @@
 
 from horovod.common.util  import is_version_greater_equal_than
 
-if is_version_greater_equal_than(tf.__version__, "2.5.0"):
+if is_version_greater_equal_than(tf.__version__, "2.6.0"):
     from keras import backend as K
     from keras import optimizers
 else:
diff --git a/horovod/tensorflow/keras/__init__.py b/horovod/tensorflow/keras/__init__.py
index 6d18bcf746..483a90fa7e 100644
--- a/horovod/tensorflow/keras/__init__.py
+++ b/horovod/tensorflow/keras/__init__.py
@@ -22,7 +22,7 @@
 
 from horovod.common.util  import is_version_greater_equal_than
 
-if is_version_greater_equal_than(tf.__version__, "2.5.0"):
+if is_version_greater_equal_than(tf.__version__, "2.6.0"):
     from keras import backend as K
 else:
     from tensorflow.python.keras import backend as K
diff --git a/horovod/tensorflow/keras/callbacks.py b/horovod/tensorflow/keras/callbacks.py
index 5e6dbeb1c0..2ee3323dfa 100644
--- a/horovod/tensorflow/keras/callbacks.py
+++ b/horovod/tensorflow/keras/callbacks.py
@@ -19,7 +19,7 @@
 
 from horovod.common.util  import is_version_greater_equal_than
 
-if is_version_greater_equal_than(tf.__version__, "2.5.0"):
+if is_version_greater_equal_than(tf.__version__, "2.6.0"):
     from keras import backend as K
 else:
     from tensorflow.python.keras import backend as K
diff --git a/test/integration/test_spark.py b/test/integration/test_spark.py
index bbca54e491..f2098a2ca6 100644
--- a/test/integration/test_spark.py
+++ b/test/integration/test_spark.py
@@ -1665,7 +1665,6 @@ def test_spark_task_service_execute_command(self):
                 file = os.path.sep.join([d, 'command_executed'])
                 self.do_test_spark_task_service_executes_command(client, file)
 
-    @mock.patch('horovod.runner.common.util.safe_shell_exec.GRACEFUL_TERMINATION_TIME_S', 0.5)
     def test_spark_task_service_abort_command(self):
         with spark_task_service(index=0) as (service, client, _):
             with tempdir() as d:
diff --git a/test/integration/test_spark_keras.py b/test/integration/test_spark_keras.py
index 2e107ea9fe..8be04c1ab8 100644
--- a/test/integration/test_spark_keras.py
+++ b/test/integration/test_spark_keras.py
@@ -72,9 +72,6 @@ def fit(model, train_data, val_data, steps_per_epoch, validation_steps, callback
     return fit
 
 
-#PR3099 [https://github.com/horovod/horovod/pull/3099] doesn't fix
-#Tensorflow>=2.6.0 tests
-@pytest.mark.skipif(LooseVersion(tf.__version__) >= LooseVersion('2.6.0'), reason='TensorFlow>=2.6.0 tests')
 class SparkKerasTests(tf.test.TestCase):
     def __init__(self, *args, **kwargs):
         super(SparkKerasTests, self).__init__(*args, **kwargs)
diff --git a/test/parallel/test_tensorflow2_keras.py b/test/parallel/test_tensorflow2_keras.py
index 6836c43185..d15fc3ad8d 100644
--- a/test/parallel/test_tensorflow2_keras.py
+++ b/test/parallel/test_tensorflow2_keras.py
@@ -29,7 +29,7 @@
 
 from horovod.common.util  import is_version_greater_equal_than
 
-if is_version_greater_equal_than(tf.__version__, "2.5.0"):
+if is_version_greater_equal_than(tf.__version__, "2.6.0"):
     from keras.optimizer_v2 import optimizer_v2
 else:
     from tensorflow.python.keras.optimizer_v2 import optimizer_v2
diff --git a/test/parallel/test_tensorflow_keras.py b/test/parallel/test_tensorflow_keras.py
index 763892c902..03e2001a08 100644
--- a/test/parallel/test_tensorflow_keras.py
+++ b/test/parallel/test_tensorflow_keras.py
@@ -28,7 +28,7 @@
 
 from horovod.common.util  import is_version_greater_equal_than
 
-if is_version_greater_equal_than(tf.__version__, "2.5.0"):
+if is_version_greater_equal_than(tf.__version__, "2.6.0"):
     from keras import backend as K
     from keras.optimizer_v2 import optimizer_v2
 else: