diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index 17d8c79994dbe..95aec64109489 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -57,7 +57,7 @@ Other enhancements
 - :meth:`.Styler.set_tooltips_class` and :meth:`.Styler.set_table_styles` amended to optionally allow certain css-string input arguments (:issue:`39564`)
 - :meth:`Series.loc.__getitem__` and :meth:`Series.loc.__setitem__` with :class:`MultiIndex` now raising helpful error message when indexer has too many dimensions (:issue:`35349`)
 - :meth:`pandas.read_stata` and :class:`StataReader` support reading data from compressed files.
-
+- Add support for parsing ``ISO 8601``-like timestamps with negative signs to :meth:`pandas.Timedelta` (:issue:`37172`)
 
 .. ---------------------------------------------------------------------------
 
diff --git a/pandas/_libs/tslibs/timedeltas.pyx b/pandas/_libs/tslibs/timedeltas.pyx
index 748a4c27e64ad..25e0941db75bd 100644
--- a/pandas/_libs/tslibs/timedeltas.pyx
+++ b/pandas/_libs/tslibs/timedeltas.pyx
@@ -276,7 +276,7 @@ cdef convert_to_timedelta64(object ts, str unit):
             ts = cast_from_unit(ts, unit)
             ts = np.timedelta64(ts, "ns")
     elif isinstance(ts, str):
-        if len(ts) > 0 and ts[0] == "P":
+        if (len(ts) > 0 and ts[0] == "P") or (len(ts) > 1 and ts[:2] == "-P"):
             ts = parse_iso_format_string(ts)
         else:
             ts = parse_timedelta_string(ts)
@@ -673,13 +673,17 @@ cdef inline int64_t parse_iso_format_string(str ts) except? -1:
     cdef:
         unicode c
         int64_t result = 0, r
-        int p = 0
+        int p = 0, sign = 1
         object dec_unit = 'ms', err_msg
         bint have_dot = 0, have_value = 0, neg = 0
         list number = [], unit = []
 
     err_msg = f"Invalid ISO 8601 Duration format - {ts}"
 
+    if ts[0] == "-":
+        sign = -1
+        ts = ts[1:]
+
     for c in ts:
         # number (ascii codes)
         if 48 <= ord(c) <= 57:
@@ -711,6 +715,8 @@ cdef inline int64_t parse_iso_format_string(str ts) except? -1:
                     raise ValueError(err_msg)
                 else:
                     neg = 1
+            elif c == "+":
+                pass
             elif c in ['W', 'D', 'H', 'M']:
                 if c in ['H', 'M'] and len(number) > 2:
                     raise ValueError(err_msg)
@@ -751,7 +757,7 @@ cdef inline int64_t parse_iso_format_string(str ts) except? -1:
         # Received string only - never parsed any values
         raise ValueError(err_msg)
 
-    return result
+    return sign*result
 
 
 cdef _to_py_int_float(v):
@@ -1252,7 +1258,9 @@ class Timedelta(_Timedelta):
         elif isinstance(value, str):
             if unit is not None:
                 raise ValueError("unit must not be specified if the value is a str")
-            if len(value) > 0 and value[0] == 'P':
+            if (len(value) > 0 and value[0] == 'P') or (
+                len(value) > 1 and value[:2] == '-P'
+            ):
                 value = parse_iso_format_string(value)
             else:
                 value = parse_timedelta_string(value)
diff --git a/pandas/tests/scalar/timedelta/test_constructors.py b/pandas/tests/scalar/timedelta/test_constructors.py
index 64d5a5e9b3fff..de7a0dc97d565 100644
--- a/pandas/tests/scalar/timedelta/test_constructors.py
+++ b/pandas/tests/scalar/timedelta/test_constructors.py
@@ -263,6 +263,9 @@ def test_construction_out_of_bounds_td64():
         ("P1W", Timedelta(days=7)),
         ("PT300S", Timedelta(seconds=300)),
         ("P1DT0H0M00000000000S", Timedelta(days=1)),
+        ("PT-6H3M", Timedelta(hours=-6, minutes=3)),
+        ("-PT6H3M", Timedelta(hours=-6, minutes=-3)),
+        ("-PT-6H+3M", Timedelta(hours=6, minutes=-3)),
     ],
 )
 def test_iso_constructor(fmt, exp):
@@ -277,6 +280,8 @@ def test_iso_constructor(fmt, exp):
         "P0DT999H999M999S",
         "P1DT0H0M0.0000000000000S",
         "P1DT0H0M0.S",
+        "P",
+        "-P",
     ],
 )
 def test_iso_constructor_raises(fmt):