diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 59c90534beefd..1a7fe0a24665d 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -92,9 +92,10 @@ Categorical
 
 Datetimelike
 ^^^^^^^^^^^^
+
 - Bug in :class:`Timestamp` where constructing :class:`Timestamp` from ambiguous epoch time and calling constructor again changed :meth:`Timestamp.value` property (:issue:`24329`)
 - :meth:`DatetimeArray.searchsorted`, :meth:`TimedeltaArray.searchsorted`, :meth:`PeriodArray.searchsorted` not recognizing non-pandas scalars and incorrectly raising ``ValueError`` instead of ``TypeError`` (:issue:`30950`)
--
+- Bug in :class:`Timestamp` where constructing :class:`Timestamp` with dateutil timezone less than 128 nanoseconds before daylight saving time switch from winter to summer would result in nonexistent time (:issue:`31043`)
 
 Timedelta
 ^^^^^^^^^
diff --git a/pandas/_libs/tslibs/nattype.pyx b/pandas/_libs/tslibs/nattype.pyx
index 67c0f0cc33ab8..61b2721696bad 100644
--- a/pandas/_libs/tslibs/nattype.pyx
+++ b/pandas/_libs/tslibs/nattype.pyx
@@ -278,7 +278,7 @@ cdef class _NaT(datetime):
 
     def total_seconds(self):
         """
-        Total duration of timedelta in seconds (to ns precision).
+        Total duration of timedelta in seconds (to microsecond precision).
         """
         # GH#10939
         return np.nan
diff --git a/pandas/_libs/tslibs/timedeltas.pyx b/pandas/_libs/tslibs/timedeltas.pyx
index 0a773b8a215ed..8f78ae6a1322e 100644
--- a/pandas/_libs/tslibs/timedeltas.pyx
+++ b/pandas/_libs/tslibs/timedeltas.pyx
@@ -861,9 +861,11 @@ cdef class _Timedelta(timedelta):
 
     def total_seconds(self):
         """
-        Total duration of timedelta in seconds (to ns precision).
+        Total duration of timedelta in seconds (to microsecond precision).
         """
-        return self.value / 1e9
+        # GH 31043
+        # Microseconds precision to avoid confusing tzinfo.utcoffset
+        return (self.value - self.value % 1000) / 1e9
 
     def view(self, dtype):
         """
diff --git a/pandas/tests/indexes/datetimes/test_timezones.py b/pandas/tests/indexes/datetimes/test_timezones.py
index df64820777f3f..c785eb67e5184 100644
--- a/pandas/tests/indexes/datetimes/test_timezones.py
+++ b/pandas/tests/indexes/datetimes/test_timezones.py
@@ -2,6 +2,7 @@
 Tests for DatetimeIndex timezone-related methods
 """
 from datetime import date, datetime, time, timedelta, tzinfo
+from distutils.version import LooseVersion
 
 import dateutil
 from dateutil.tz import gettz, tzlocal
@@ -10,6 +11,7 @@
 import pytz
 
 from pandas._libs.tslibs import conversion, timezones
+from pandas.compat._optional import _get_version
 import pandas.util._test_decorators as td
 
 import pandas as pd
@@ -585,7 +587,10 @@ def test_dti_construction_ambiguous_endpoint(self, tz):
                 "dateutil/US/Pacific",
                 "shift_backward",
                 "2019-03-10 01:00",
-                marks=pytest.mark.xfail(reason="GH 24329"),
+                marks=pytest.mark.xfail(
+                    LooseVersion(_get_version(dateutil)) < LooseVersion("2.7.0"),
+                    reason="GH 31043",
+                ),
             ),
             ["US/Pacific", timedelta(hours=1), "2019-03-10 03:00"],
         ],
diff --git a/pandas/tests/scalar/timestamp/test_timestamp.py b/pandas/tests/scalar/timestamp/test_timestamp.py
index c60406fdbc8a6..b70948318e39e 100644
--- a/pandas/tests/scalar/timestamp/test_timestamp.py
+++ b/pandas/tests/scalar/timestamp/test_timestamp.py
@@ -2,6 +2,7 @@
 
 import calendar
 from datetime import datetime, timedelta
+from distutils.version import LooseVersion
 import locale
 import unicodedata
 
@@ -1092,3 +1093,23 @@ def test_constructor_ambigous_dst():
     expected = ts.value
     result = Timestamp(ts).value
     assert result == expected
+
+
+@pytest.mark.xfail(
+    LooseVersion(compat._optional._get_version(dateutil)) < LooseVersion("2.7.0"),
+    reason="dateutil moved to Timedelta.total_seconds() in 2.7.0",
+)
+@pytest.mark.parametrize("epoch", [1552211999999999872, 1552211999999999999])
+def test_constructor_before_dst_switch(epoch):
+    # GH 31043
+    # Make sure that calling Timestamp constructor
+    # on time just before DST switch doesn't lead to
+    # nonexistent time or value change
+    # Works only with dateutil >= 2.7.0 as dateutil overrid
+    # pandas.Timedelta.total_seconds with
+    # datetime.timedelta.total_seconds before
+    ts = Timestamp(epoch, tz="dateutil/US/Pacific")
+    result = ts.tz.dst(ts)
+    expected = timedelta(seconds=0)
+    assert Timestamp(ts).value == epoch
+    assert result == expected