diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index 17cdb7538dad2..311dfa244f780 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -587,6 +587,7 @@ Datetimelike
 - Bug in :meth:`Series.isin` with ``datetime64[ns]`` dtype and :meth:`.DatetimeIndex.isin` incorrectly casting integers to datetimes (:issue:`36621`)
 - Bug in :meth:`Series.isin` with ``datetime64[ns]`` dtype and :meth:`.DatetimeIndex.isin` failing to consider timezone-aware and timezone-naive datetimes as always different (:issue:`35728`)
 - Bug in :meth:`Series.isin` with ``PeriodDtype`` dtype and :meth:`PeriodIndex.isin` failing to consider arguments with different ``PeriodDtype`` as always different (:issue:`37528`)
+- Bug in :class:`Period` constructor now correctly handles nanoseconds in the ``value`` argument (:issue:`34621` and :issue:`17053`)
 
 Timedelta
 ^^^^^^^^^
diff --git a/pandas/_libs/tslibs/period.pyx b/pandas/_libs/tslibs/period.pyx
index d83138528a6f9..cbd4e2e6704a9 100644
--- a/pandas/_libs/tslibs/period.pyx
+++ b/pandas/_libs/tslibs/period.pyx
@@ -2345,6 +2345,7 @@ class Period(_Period):
 
         if freq is not None:
             freq = cls._maybe_convert_freq(freq)
+        nanosecond = 0
 
         if ordinal is not None and value is not None:
             raise ValueError("Only value or ordinal but not both should be "
@@ -2394,6 +2395,14 @@ class Period(_Period):
                 value = str(value)
             value = value.upper()
             dt, reso = parse_time_string(value, freq)
+            try:
+                ts = Timestamp(value)
+            except ValueError:
+                nanosecond = 0
+            else:
+                nanosecond = ts.nanosecond
+                if nanosecond != 0:
+                    reso = 'nanosecond'
             if dt is NaT:
                 ordinal = NPY_NAT
 
@@ -2425,7 +2434,7 @@ class Period(_Period):
             base = freq_to_dtype_code(freq)
             ordinal = period_ordinal(dt.year, dt.month, dt.day,
                                      dt.hour, dt.minute, dt.second,
-                                     dt.microsecond, 0, base)
+                                     dt.microsecond, 1000*nanosecond, base)
 
         return cls._from_ordinal(ordinal, freq)
 
diff --git a/pandas/tests/scalar/period/test_period.py b/pandas/tests/scalar/period/test_period.py
index bce42f8c6caf0..9b87e32510b41 100644
--- a/pandas/tests/scalar/period/test_period.py
+++ b/pandas/tests/scalar/period/test_period.py
@@ -487,6 +487,22 @@ def test_period_cons_combined(self):
         with pytest.raises(ValueError, match=msg):
             Period("2011-01", freq="1D1W")
 
+    @pytest.mark.parametrize("day", ["1970/01/01 ", "2020-12-31 ", "1981/09/13 "])
+    @pytest.mark.parametrize("hour", ["00:00:00", "00:00:01", "23:59:59", "12:00:59"])
+    @pytest.mark.parametrize(
+        "sec_float, expected",
+        [
+            (".000000001", 1),
+            (".000000999", 999),
+            (".123456789", 789),
+            (".999999999", 999),
+        ],
+    )
+    def test_period_constructor_nanosecond(self, day, hour, sec_float, expected):
+        # GH 34621
+
+        assert Period(day + hour + sec_float).start_time.nanosecond == expected
+
     @pytest.mark.parametrize("hour", range(24))
     def test_period_large_ordinal(self, hour):
         # Issue #36430