diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index abe472cc6bb..412833a8525 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -36,6 +36,10 @@ Bug fixes
 - Fix regression introduced in v0.14.0 that would cause a crash if dask is installed
   but cloudpickle isn't (:issue:`3401`) by `Rhys Doyle <https://github.com/rdoyle45>`_
 
+- Sync with cftime by removing `dayofwk=-1` for cftime>=1.0.4. 
+   By `Anderson Banihirwe <https://github.com/andersy005>`_.
+
+
 Documentation
 ~~~~~~~~~~~~~
 
diff --git a/xarray/coding/cftime_offsets.py b/xarray/coding/cftime_offsets.py
index af46510f7c4..8471ed1a558 100644
--- a/xarray/coding/cftime_offsets.py
+++ b/xarray/coding/cftime_offsets.py
@@ -50,6 +50,7 @@
 from ..core.pdcompat import count_not_none
 from .cftimeindex import CFTimeIndex, _parse_iso8601_with_reso
 from .times import format_cftime_datetime
+from distutils.version import LooseVersion
 
 
 def get_date_type(calendar):
@@ -222,6 +223,8 @@ def _adjust_n_years(other, n, month, reference_day):
 def _shift_month(date, months, day_option="start"):
     """Shift the date to a month start or end a given number of months away.
     """
+    import cftime
+
     delta_year = (date.month + months) // 12
     month = (date.month + months) % 12
 
@@ -237,11 +240,14 @@ def _shift_month(date, months, day_option="start"):
         day = _days_in_month(reference)
     else:
         raise ValueError(day_option)
-    # dayofwk=-1 is required to update the dayofwk and dayofyr attributes of
-    # the returned date object in versions of cftime between 1.0.2 and
-    # 1.0.3.4.  It can be removed for versions of cftime greater than
-    # 1.0.3.4.
-    return date.replace(year=year, month=month, day=day, dayofwk=-1)
+    if LooseVersion(cftime.__version__) < LooseVersion("1.0.4"):
+        # dayofwk=-1 is required to update the dayofwk and dayofyr attributes of
+        # the returned date object in versions of cftime between 1.0.2 and
+        # 1.0.3.4.  It can be removed for versions of cftime greater than
+        # 1.0.3.4.
+        return date.replace(year=year, month=month, day=day, dayofwk=-1)
+    else:
+        return date.replace(year=year, month=month, day=day)
 
 
 def roll_qtrday(other, n, month, day_option, modby=3):
diff --git a/xarray/coding/cftimeindex.py b/xarray/coding/cftimeindex.py
index 434d55d6569..559c5e16287 100644
--- a/xarray/coding/cftimeindex.py
+++ b/xarray/coding/cftimeindex.py
@@ -96,6 +96,8 @@ def parse_iso8601(datetime_string):
 
 
 def _parse_iso8601_with_reso(date_type, timestr):
+    import cftime
+
     default = date_type(1, 1, 1)
     result = parse_iso8601(timestr)
     replace = {}
@@ -107,12 +109,12 @@ def _parse_iso8601_with_reso(date_type, timestr):
             # TODO: Consider adding support for sub-second resolution?
             replace[attr] = int(value)
             resolution = attr
-
-    # dayofwk=-1 is required to update the dayofwk and dayofyr attributes of
-    # the returned date object in versions of cftime between 1.0.2 and
-    # 1.0.3.4.  It can be removed for versions of cftime greater than
-    # 1.0.3.4.
-    replace["dayofwk"] = -1
+    if LooseVersion(cftime.__version__) < LooseVersion("1.0.4"):
+        # dayofwk=-1 is required to update the dayofwk and dayofyr attributes of
+        # the returned date object in versions of cftime between 1.0.2 and
+        # 1.0.3.4.  It can be removed for versions of cftime greater than
+        # 1.0.3.4.
+        replace["dayofwk"] = -1
     return default.replace(**replace), resolution