diff --git a/src/apify/_actor.py b/src/apify/_actor.py
index e1acf238..13dc3885 100644
--- a/src/apify/_actor.py
+++ b/src/apify/_actor.py
@@ -1,6 +1,7 @@
 from __future__ import annotations
 
 import asyncio
+import math
 import sys
 import warnings
 from contextlib import suppress
@@ -1467,9 +1468,16 @@ def _get_default_exit_process(self) -> bool:
         return True
 
     def _get_remaining_time(self) -> timedelta | None:
-        """Get time remaining from the Actor timeout. Returns `None` if not on an Apify platform."""
+        """Get time remaining from the Actor timeout, rounded up to whole seconds with minimum value of 1 second.
+
+        API treats 0 second timeout as no timeout, the minimum acceptable timeout is 1 second.
+
+        Returns `None` if not on an Apify platform.
+        """
+        smallest_possible_api_timeout = 1
         if self.is_at_home() and self.configuration.timeout_at:
-            return max(self.configuration.timeout_at - datetime.now(tz=UTC), timedelta(0))
+            remaining = self.configuration.timeout_at - datetime.now(tz=UTC)
+            return timedelta(seconds=max(math.ceil(remaining.total_seconds()), smallest_possible_api_timeout))
 
         self.log.warning(
             'Using the `inherit` argument is only possible when the Actor is running on the Apify platform and '
diff --git a/tests/unit/actor/test_actor_helpers.py b/tests/unit/actor/test_actor_helpers.py
index 78c567c6..2078b7f3 100644
--- a/tests/unit/actor/test_actor_helpers.py
+++ b/tests/unit/actor/test_actor_helpers.py
@@ -4,7 +4,7 @@
 import logging
 from datetime import UTC, datetime, timedelta
 from typing import TYPE_CHECKING
-from unittest.mock import AsyncMock, patch
+from unittest.mock import AsyncMock, Mock, patch
 
 import pytest
 
@@ -316,15 +316,15 @@ async def test_get_remaining_time_warns_when_not_at_home(caplog: pytest.LogCaptu
     assert any('inherit' in msg for msg in caplog.messages)
 
 
-async def test_get_remaining_time_clamps_negative_to_zero() -> None:
-    """Test that _get_remaining_time returns timedelta(0) instead of a negative value when timeout is in the past."""
+async def test_get_remaining_time_clamps_negative_to_one() -> None:
+    """Test that _get_remaining_time returns 1 second instead of a negative value when timeout is in the past."""
     async with Actor:
         Actor.configuration.is_at_home = True
         Actor.configuration.timeout_at = datetime.now(tz=UTC) - timedelta(minutes=5)
 
         result = Actor._get_remaining_time()
         assert result is not None
-        assert result == timedelta(0)
+        assert result == timedelta(seconds=1)
 
 
 async def test_get_remaining_time_returns_positive_when_timeout_in_future() -> None:
@@ -339,6 +339,38 @@ async def test_get_remaining_time_returns_positive_when_timeout_in_future() -> N
         assert result <= timedelta(minutes=5)
 
 
+@pytest.mark.parametrize('method_name', ['start', 'call'])
+async def test_actor_start_and_call_skipped_when_no_inherited_time_remains(
+    apify_client_async_patcher: ApifyClientAsyncPatcher,
+    method_name: str,
+) -> None:
+    """Test that Actor.start/Actor.call with `timeout='inherit'` is skipped when the run is past its timeout."""
+    apify_client_async_patcher.patch('actor', method_name, return_value=Mock())
+
+    async with Actor:
+        Actor.configuration.is_at_home = True
+        Actor.configuration.timeout_at = datetime.now(tz=UTC) - timedelta(minutes=5)
+        await getattr(Actor, method_name)('some-actor-id', timeout='inherit')
+
+    assert len(apify_client_async_patcher.calls['actor'][method_name]) == 1
+    assert apify_client_async_patcher.calls['actor'][method_name][0][1]['run_timeout'] == timedelta(seconds=1)
+
+
+async def test_actor_call_task_skipped_when_no_inherited_time_remains(
+    apify_client_async_patcher: ApifyClientAsyncPatcher,
+) -> None:
+    """Test that Actor.call_task with `timeout='inherit'` is skipped when the run is past its timeout."""
+    apify_client_async_patcher.patch('task', 'call', return_value=Mock())
+
+    async with Actor:
+        Actor.configuration.is_at_home = True
+        Actor.configuration.timeout_at = datetime.now(tz=UTC) - timedelta(minutes=5)
+        await Actor.call_task('some-task-id', timeout='inherit')
+
+    assert len(apify_client_async_patcher.calls['task']['call']) == 1
+    assert apify_client_async_patcher.calls['task']['call'][0][1]['run_timeout'] == timedelta(seconds=1)
+
+
 async def test_reboot_runs_all_listeners_even_when_one_fails(
     apify_client_async_patcher: ApifyClientAsyncPatcher,
     caplog: pytest.LogCaptureFixture,