diff --git a/src/huggingface_hub/inference/_client.py b/src/huggingface_hub/inference/_client.py
index ab3c61542f..dbb336a421 100644
--- a/src/huggingface_hub/inference/_client.py
+++ b/src/huggingface_hub/inference/_client.py
@@ -188,7 +188,7 @@ def __init__(
                 " It has the exact same behavior as `token`."
             )
 
-        self.model: Optional[str] = model
+        self.model: Optional[str] = base_url or model
         self.token: Optional[str] = token if token is not None else api_key
         self.headers = headers if headers is not None else {}
 
@@ -199,9 +199,6 @@ def __init__(
         self.timeout = timeout
         self.proxies = proxies
 
-        # OpenAI compatibility
-        self.base_url = base_url
-
     def __repr__(self):
         return f"<InferenceClient(model='{self.model if self.model else ''}', timeout={self.timeout})>"
 
@@ -328,9 +325,12 @@ def _inner_post(
                 return response.iter_lines() if stream else response.content
             except HTTPError as error:
                 if error.response.status_code == 422 and request_parameters.task != "unknown":
-                    error.args = (
-                        f"{error.args[0]}\nMake sure '{request_parameters.task}' task is supported by the model.",
-                    ) + error.args[1:]
+                    msg = str(error.args[0])
+                    print(error.response.text)
+                    if len(error.response.text) > 0:
+                        msg += f"\n{error.response.text}\n"
+                    msg += f"\nMake sure '{request_parameters.task}' task is supported by the model."
+                    error.args = (msg,) + error.args[1:]
                 if error.response.status_code == 503:
                     # If Model is unavailable, either raise a TimeoutError...
                     if timeout is not None and time.time() - t0 > timeout:
@@ -934,9 +934,9 @@ def chat_completion(
         provider_helper = get_provider_helper(self.provider, task="conversational")
 
         # Since `chat_completion(..., model=xxx)` is also a payload parameter for the server, we need to handle 'model' differently.
-        # `self.base_url` and `self.model` takes precedence over 'model' argument for building URL.
+        # `self.model` takes precedence over 'model' argument for building URL.
         # `model` takes precedence for payload value.
-        model_id_or_url = self.base_url or self.model or model
+        model_id_or_url = self.model or model
         payload_model = model or self.model
 
         # Prepare the payload
diff --git a/src/huggingface_hub/inference/_generated/_async_client.py b/src/huggingface_hub/inference/_generated/_async_client.py
index cd419b0b60..6f111e68ba 100644
--- a/src/huggingface_hub/inference/_generated/_async_client.py
+++ b/src/huggingface_hub/inference/_generated/_async_client.py
@@ -179,7 +179,7 @@ def __init__(
                 " It has the exact same behavior as `token`."
             )
 
-        self.model: Optional[str] = model
+        self.model: Optional[str] = base_url or model
         self.token: Optional[str] = token if token is not None else api_key
         self.headers = headers if headers is not None else {}
 
@@ -191,9 +191,6 @@ def __init__(
         self.trust_env = trust_env
         self.proxies = proxies
 
-        # OpenAI compatibility
-        self.base_url = base_url
-
         # Keep track of the sessions to close them properly
         self._sessions: Dict["ClientSession", Set["ClientResponse"]] = dict()
 
@@ -977,9 +974,9 @@ async def chat_completion(
         provider_helper = get_provider_helper(self.provider, task="conversational")
 
         # Since `chat_completion(..., model=xxx)` is also a payload parameter for the server, we need to handle 'model' differently.
-        # `self.base_url` and `self.model` takes precedence over 'model' argument for building URL.
+        # `self.model` takes precedence over 'model' argument for building URL.
         # `model` takes precedence for payload value.
-        model_id_or_url = self.base_url or self.model or model
+        model_id_or_url = self.model or model
         payload_model = model or self.model
 
         # Prepare the payload
diff --git a/tests/test_inference_client.py b/tests/test_inference_client.py
index 5a41baa094..c5437e46bd 100644
--- a/tests/test_inference_client.py
+++ b/tests/test_inference_client.py
@@ -1186,3 +1186,12 @@ def test_chat_completion_error_in_stream():
 def test_resolve_chat_completion_url(model_url: str, expected_url: str):
     url = _build_chat_completion_url(model_url)
     assert url == expected_url
+
+
+def test_pass_url_as_base_url():
+    client = InferenceClient(base_url="http://localhost:8082/v1/")
+    provider = get_provider_helper("hf-inference", "text-generation")
+    request = provider.prepare_request(
+        inputs="The huggingface_hub library is ", parameters={}, headers={}, model=client.model, api_key=None
+    )
+    assert request.url == "http://localhost:8082/v1/"