diff --git a/pandas/_libs/index.pyi b/pandas/_libs/index.pyi
index 9f526dd3fe653..752f339ff31da 100644
--- a/pandas/_libs/index.pyi
+++ b/pandas/_libs/index.pyi
@@ -18,12 +18,6 @@ class IndexEngine:
     def is_monotonic_increasing(self) -> bool: ...
     @property
     def is_monotonic_decreasing(self) -> bool: ...
-    def get_backfill_indexer(
-        self, other: np.ndarray, limit: int | None = ...
-    ) -> npt.NDArray[np.intp]: ...
-    def get_pad_indexer(
-        self, other: np.ndarray, limit: int | None = ...
-    ) -> npt.NDArray[np.intp]: ...
     @property
     def is_mapping_populated(self) -> bool: ...
     def clear_mapping(self): ...
diff --git a/pandas/_libs/index.pyx b/pandas/_libs/index.pyx
index cc6a2ad10f020..a25d15dc68f9a 100644
--- a/pandas/_libs/index.pyx
+++ b/pandas/_libs/index.pyx
@@ -224,12 +224,6 @@ cdef class IndexEngine:
     cdef _call_monotonic(self, values):
         return algos.is_monotonic(values, timelike=False)
 
-    def get_backfill_indexer(self, other: np.ndarray, limit=None) -> np.ndarray:
-        return algos.backfill(self.values, other, limit=limit)
-
-    def get_pad_indexer(self, other: np.ndarray, limit=None) -> np.ndarray:
-        return algos.pad(self.values, other, limit=limit)
-
     cdef _make_hash_table(self, Py_ssize_t n):
         raise NotImplementedError
 
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index a8de95cfa72e0..cf253ca598c18 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -3703,13 +3703,14 @@ def _get_fill_indexer(
             )
 
         if self.is_monotonic_increasing and target.is_monotonic_increasing:
-            engine_method = (
-                self._engine.get_pad_indexer
-                if method == "pad"
-                else self._engine.get_backfill_indexer
-            )
             target_values = target._get_engine_target()
-            indexer = engine_method(target_values, limit)
+            own_values = self._get_engine_target()
+
+            if method == "pad":
+                indexer = libalgos.pad(own_values, target_values, limit=limit)
+            else:
+                # i.e. "backfill"
+                indexer = libalgos.backfill(own_values, target_values, limit=limit)
         else:
             indexer = self._get_fill_indexer_searchsorted(target, method, limit)
         if tolerance is not None and len(self):
diff --git a/pandas/tests/indexes/test_engines.py b/pandas/tests/indexes/test_engines.py
index 45e8e56d46381..785db921dbab4 100644
--- a/pandas/tests/indexes/test_engines.py
+++ b/pandas/tests/indexes/test_engines.py
@@ -3,13 +3,9 @@
 import numpy as np
 import pytest
 
-from pandas._libs import (
-    algos as libalgos,
-    index as libindex,
-)
+from pandas._libs import index as libindex
 
 import pandas as pd
-import pandas._testing as tm
 
 
 @pytest.fixture(
@@ -145,30 +141,6 @@ def test_get_loc(self, numeric_indexing_engine_type_and_dtype):
         result = engine.get_loc(2)
         assert (result == expected).all()
 
-    def test_get_backfill_indexer(self, numeric_indexing_engine_type_and_dtype):
-        engine_type, dtype = numeric_indexing_engine_type_and_dtype
-
-        arr = np.array([1, 5, 10], dtype=dtype)
-        engine = engine_type(arr)
-
-        new = np.arange(12, dtype=dtype)
-        result = engine.get_backfill_indexer(new)
-
-        expected = libalgos.backfill(arr, new)
-        tm.assert_numpy_array_equal(result, expected)
-
-    def test_get_pad_indexer(self, numeric_indexing_engine_type_and_dtype):
-        engine_type, dtype = numeric_indexing_engine_type_and_dtype
-
-        arr = np.array([1, 5, 10], dtype=dtype)
-        engine = engine_type(arr)
-
-        new = np.arange(12, dtype=dtype)
-        result = engine.get_pad_indexer(new)
-
-        expected = libalgos.pad(arr, new)
-        tm.assert_numpy_array_equal(result, expected)
-
 
 class TestObjectEngine:
     engine_type = libindex.ObjectEngine
@@ -225,23 +197,3 @@ def test_get_loc(self):
         expected = np.array([False, True, False] * num, dtype=bool)
         result = engine.get_loc("b")
         assert (result == expected).all()
-
-    def test_get_backfill_indexer(self):
-        arr = np.array(["a", "e", "j"], dtype=self.dtype)
-        engine = self.engine_type(arr)
-
-        new = np.array(list("abcdefghij"), dtype=self.dtype)
-        result = engine.get_backfill_indexer(new)
-
-        expected = libalgos.backfill["object"](arr, new)
-        tm.assert_numpy_array_equal(result, expected)
-
-    def test_get_pad_indexer(self):
-        arr = np.array(["a", "e", "j"], dtype=self.dtype)
-        engine = self.engine_type(arr)
-
-        new = np.array(list("abcdefghij"), dtype=self.dtype)
-        result = engine.get_pad_indexer(new)
-
-        expected = libalgos.pad["object"](arr, new)
-        tm.assert_numpy_array_equal(result, expected)