diff --git a/src/agents/models/openai_provider.py b/src/agents/models/openai_provider.py
index 91f2366bc..91eeaccc8 100644
--- a/src/agents/models/openai_provider.py
+++ b/src/agents/models/openai_provider.py
@@ -81,13 +81,17 @@ def _get_client(self) -> AsyncOpenAI:
         return self._client
 
     def get_model(self, model_name: str | None) -> Model:
-        if model_name is None:
-            model_name = get_default_model()
+        model_is_explicit = model_name is not None
+        resolved_model_name = model_name if model_name is not None else get_default_model()
 
         client = self._get_client()
 
         return (
-            OpenAIResponsesModel(model=model_name, openai_client=client)
+            OpenAIResponsesModel(
+                model=resolved_model_name,
+                openai_client=client,
+                model_is_explicit=model_is_explicit,
+            )
             if self._use_responses
-            else OpenAIChatCompletionsModel(model=model_name, openai_client=client)
+            else OpenAIChatCompletionsModel(model=resolved_model_name, openai_client=client)
         )
diff --git a/src/agents/models/openai_responses.py b/src/agents/models/openai_responses.py
index 4588937cb..a8695c89c 100644
--- a/src/agents/models/openai_responses.py
+++ b/src/agents/models/openai_responses.py
@@ -67,8 +67,11 @@ def __init__(
         self,
         model: str | ChatModel,
         openai_client: AsyncOpenAI,
+        *,
+        model_is_explicit: bool = True,
     ) -> None:
         self.model = model
+        self._model_is_explicit = model_is_explicit
         self._client = openai_client
 
     def _non_null_or_omit(self, value: Any) -> Any:
@@ -262,6 +265,12 @@ async def _fetch_response(
         converted_tools = Converter.convert_tools(tools, handoffs)
         converted_tools_payload = _to_dump_compatible(converted_tools.tools)
         response_format = Converter.get_response_format(output_schema)
+        should_omit_model = prompt is not None and not self._model_is_explicit
+        model_param: str | ChatModel | Omit = self.model if not should_omit_model else omit
+        should_omit_tools = prompt is not None and len(converted_tools_payload) == 0
+        tools_param: list[ToolParam] | Omit = (
+            converted_tools_payload if not should_omit_tools else omit
+        )
 
         include_set: set[str] = set(converted_tools.includes)
         if model_settings.response_include is not None:
@@ -309,10 +318,10 @@ async def _fetch_response(
             previous_response_id=self._non_null_or_omit(previous_response_id),
             conversation=self._non_null_or_omit(conversation_id),
             instructions=self._non_null_or_omit(system_instructions),
-            model=self.model,
+            model=model_param,
             input=list_input,
             include=include,
-            tools=converted_tools_payload,
+            tools=tools_param,
             prompt=self._non_null_or_omit(prompt),
             temperature=self._non_null_or_omit(model_settings.temperature),
             top_p=self._non_null_or_omit(model_settings.top_p),
diff --git a/tests/test_agent_prompt.py b/tests/test_agent_prompt.py
index 3d5ed5a3f..e3ed40fbe 100644
--- a/tests/test_agent_prompt.py
+++ b/tests/test_agent_prompt.py
@@ -1,8 +1,13 @@
+from __future__ import annotations
+
 import pytest
+from openai import omit
 
-from agents import Agent, Prompt, RunContextWrapper, Runner
+from agents import Agent, Prompt, RunConfig, RunContextWrapper, Runner
+from agents.models.interface import Model, ModelProvider
+from agents.models.openai_responses import OpenAIResponsesModel
 
-from .fake_model import FakeModel
+from .fake_model import FakeModel, get_response_obj
 from .test_responses import get_text_message
 
 
@@ -97,3 +102,43 @@ async def test_prompt_is_passed_to_model():
         "variables": None,
     }
     assert model.last_prompt == expected_prompt
+
+
+class _SingleModelProvider(ModelProvider):
+    def __init__(self, model: Model):
+        self._model = model
+
+    def get_model(self, model_name: str | None) -> Model:
+        return self._model
+
+
+@pytest.mark.allow_call_model_methods
+@pytest.mark.asyncio
+async def test_agent_prompt_with_default_model_omits_model_and_tools_parameters():
+    called_kwargs: dict[str, object] = {}
+
+    class DummyResponses:
+        async def create(self, **kwargs):
+            nonlocal called_kwargs
+            called_kwargs = kwargs
+            return get_response_obj([get_text_message("done")])
+
+    class DummyResponsesClient:
+        def __init__(self):
+            self.responses = DummyResponses()
+
+    model = OpenAIResponsesModel(
+        model="gpt-4.1",
+        openai_client=DummyResponsesClient(),  # type: ignore[arg-type]
+        model_is_explicit=False,
+    )
+
+    run_config = RunConfig(model_provider=_SingleModelProvider(model))
+    agent = Agent(name="prompt-agent", prompt={"id": "pmpt_agent"})
+
+    await Runner.run(agent, input="hi", run_config=run_config)
+
+    expected_prompt = {"id": "pmpt_agent", "version": None, "variables": None}
+    assert called_kwargs["prompt"] == expected_prompt
+    assert called_kwargs["model"] is omit
+    assert called_kwargs["tools"] is omit
diff --git a/tests/test_openai_responses.py b/tests/test_openai_responses.py
index 0823d3cac..ecd509ac6 100644
--- a/tests/test_openai_responses.py
+++ b/tests/test_openai_responses.py
@@ -3,6 +3,7 @@
 from typing import Any
 
 import pytest
+from openai import omit
 from openai.types.responses import ResponseCompletedEvent
 
 from agents import ModelSettings, ModelTracing, __version__
@@ -63,3 +64,74 @@ def __init__(self):
 
     assert "extra_headers" in called_kwargs
     assert called_kwargs["extra_headers"]["User-Agent"] == expected_ua
+
+
+@pytest.mark.allow_call_model_methods
+@pytest.mark.asyncio
+async def test_prompt_id_omits_model_parameter():
+    called_kwargs: dict[str, Any] = {}
+
+    class DummyResponses:
+        async def create(self, **kwargs):
+            nonlocal called_kwargs
+            called_kwargs = kwargs
+            return get_response_obj([])
+
+    class DummyResponsesClient:
+        def __init__(self):
+            self.responses = DummyResponses()
+
+    model = OpenAIResponsesModel(
+        model="gpt-4",
+        openai_client=DummyResponsesClient(),  # type: ignore[arg-type]
+        model_is_explicit=False,
+    )
+
+    await model.get_response(
+        system_instructions=None,
+        input="hi",
+        model_settings=ModelSettings(),
+        tools=[],
+        output_schema=None,
+        handoffs=[],
+        tracing=ModelTracing.DISABLED,
+        prompt={"id": "pmpt_123"},
+    )
+
+    assert called_kwargs["prompt"] == {"id": "pmpt_123"}
+    assert called_kwargs["model"] is omit
+
+
+@pytest.mark.allow_call_model_methods
+@pytest.mark.asyncio
+async def test_prompt_id_omits_tools_parameter_when_no_tools_configured():
+    called_kwargs: dict[str, Any] = {}
+
+    class DummyResponses:
+        async def create(self, **kwargs):
+            nonlocal called_kwargs
+            called_kwargs = kwargs
+            return get_response_obj([])
+
+    class DummyResponsesClient:
+        def __init__(self):
+            self.responses = DummyResponses()
+
+    model = OpenAIResponsesModel(
+        model="gpt-4",
+        openai_client=DummyResponsesClient(),  # type: ignore[arg-type]
+        model_is_explicit=False,
+    )
+
+    await model.get_response(
+        system_instructions=None,
+        input="hi",
+        model_settings=ModelSettings(),
+        tools=[],
+        output_schema=None,
+        handoffs=[],
+        tracing=ModelTracing.DISABLED,
+        prompt={"id": "pmpt_123"},
+    )
+
+    assert called_kwargs["tools"] is omit