diff --git a/tornado/curl_httpclient.py b/tornado/curl_httpclient.py
index ecaf13794..b7f482033 100644
--- a/tornado/curl_httpclient.py
+++ b/tornado/curl_httpclient.py
@@ -61,15 +61,6 @@ def initialize(  # type: ignore
         self._fds: dict[int, int] = {}
         self._timeout: object | None = None
 
-        # libcurl has bugs that sometimes cause it to not report all
-        # relevant file descriptors and timeouts to TIMERFUNCTION/
-        # SOCKETFUNCTION.  Mitigate the effects of such bugs by
-        # forcing a periodic scan of all active requests.
-        self._force_timeout_callback = ioloop.PeriodicCallback(
-            self._handle_force_timeout, 1000
-        )
-        self._force_timeout_callback.start()
-
         # Work around a bug in libcurl 7.29.0: Some fields in the curl
         # multi object are initialized lazily, and its destructor will
         # segfault if it is destroyed without having been used.  Add
@@ -80,7 +71,6 @@ def initialize(  # type: ignore
         self._multi.remove_handle(dummy_curl_handle)
 
     def close(self) -> None:
-        self._force_timeout_callback.stop()
         if self._timeout is not None:
             self.io_loop.remove_timeout(self._timeout)
         for curl in self._curls:
@@ -91,7 +81,6 @@ def close(self) -> None:
         # Set below properties to None to reduce the reference count of current
         # instance, because those properties hold some methods of current
         # instance that will case circular reference.
-        self._force_timeout_callback = None  # type: ignore
         self._multi = None
 
     def fetch_impl(
@@ -185,19 +174,6 @@ def _handle_timeout(self) -> None:
         if new_timeout >= 0:
             self._set_timeout(new_timeout)
 
-    def _handle_force_timeout(self) -> None:
-        """Called by IOLoop periodically to ask libcurl to process any
-        events it may have forgotten about.
-        """
-        while True:
-            try:
-                ret, num_handles = self._multi.socket_all()
-            except pycurl.error as e:
-                ret = e.args[0]
-            if ret != pycurl.E_CALL_MULTI_PERFORM:
-                break
-        self._finish_pending_requests()
-
     def _finish_pending_requests(self) -> None:
         """Process any requests that were completed by the last
         call to multi.socket_action.
@@ -487,12 +463,12 @@ def write_function(b: bytes | bytearray) -> int:
                 raise ValueError("Body must be None for GET request")
             request_buffer = BytesIO(utf8(request.body or ""))
 
-            def ioctl(cmd: int) -> None:
-                if cmd == curl.IOCMD_RESTARTREAD:  # type: ignore
-                    request_buffer.seek(0)
+            def seek(offset: int, origin: int) -> int:
+                request_buffer.seek(offset, origin)
+                return pycurl.SEEKFUNC_OK
 
             curl.setopt(pycurl.READFUNCTION, request_buffer.read)
-            curl.setopt(pycurl.IOCTLFUNCTION, ioctl)
+            curl.setopt(pycurl.SEEKFUNCTION, seek)
             if request.method == "POST":
                 curl.setopt(pycurl.POSTFIELDSIZE, len(request.body or ""))
             else: