diff --git a/pandas/_libs/tslibs/period.pyx b/pandas/_libs/tslibs/period.pyx
index 47ebf139ed496..cb0fd7d1aa380 100644
--- a/pandas/_libs/tslibs/period.pyx
+++ b/pandas/_libs/tslibs/period.pyx
@@ -2355,6 +2355,7 @@ 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 "
@@ -2404,6 +2405,14 @@ 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
 
@@ -2435,7 +2444,7 @@ 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 702899f163e06..52f46a2767b45 100644
--- a/pandas/tests/scalar/period/test_period.py
+++ b/pandas/tests/scalar/period/test_period.py
@@ -484,6 +484,22 @@ 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(
+        "floating_sec_, expected",
+        [
+            (".000000001", 1),
+            (".000000999", 999),
+            (".123456789", 789),
+            (".999999999", 999),
+        ],
+    )
+    def test_period_constructor_nanosecond(self, day_, hour_, floating_sec_, expected):
+        # GH 34621
+        result = Period(day_ + hour_ + floating_sec_).start_time.nanosecond
+        assert result == expected
+
 
 class TestPeriodMethods:
     def test_round_trip(self):