diff --git a/CHANGES.rst b/CHANGES.rst
index 521f5a08a..2b8179855 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -43,6 +43,8 @@ Unreleased
 -   ``urlize`` does not add ``mailto:`` to values like `@a@b`. :pr:`1870`
 -   Tests decorated with `@pass_context`` can be used with the ``|select``
     filter. :issue:`1624`
+-   Using ``set`` for multiple assignment (``a, b = 1, 2``) does not fail when the
+    target is a namespace attribute. :issue:`1413`
 
 
 Version 3.1.4
diff --git a/docs/templates.rst b/docs/templates.rst
index 8db8ccaf9..9f376a13c 100644
--- a/docs/templates.rst
+++ b/docs/templates.rst
@@ -1678,6 +1678,9 @@ The following functions are available in the global scope by default:
 
     .. versionadded:: 2.10
 
+    .. versionchanged:: 3.2
+        Namespace attributes can be assigned to in multiple assignment.
+
 
 Extensions
 ----------
diff --git a/src/jinja2/compiler.py b/src/jinja2/compiler.py
index ca079070a..a4ff6a1b1 100644
--- a/src/jinja2/compiler.py
+++ b/src/jinja2/compiler.py
@@ -1581,6 +1581,29 @@ def visit_Output(self, node: nodes.Output, frame: Frame) -> None:
 
     def visit_Assign(self, node: nodes.Assign, frame: Frame) -> None:
         self.push_assign_tracking()
+
+        # ``a.b`` is allowed for assignment, and is parsed as an NSRef. However,
+        # it is only valid if it references a Namespace object. Emit a check for
+        # that for each ref here, before assignment code is emitted. This can't
+        # be done in visit_NSRef as the ref could be in the middle of a tuple.
+        seen_refs: t.Set[str] = set()
+
+        for nsref in node.find_all(nodes.NSRef):
+            if nsref.name in seen_refs:
+                # Only emit the check for each reference once, in case the same
+                # ref is used multiple times in a tuple, `ns.a, ns.b = c, d`.
+                continue
+
+            seen_refs.add(nsref.name)
+            ref = frame.symbols.ref(nsref.name)
+            self.writeline(f"if not isinstance({ref}, Namespace):")
+            self.indent()
+            self.writeline(
+                "raise TemplateRuntimeError"
+                '("cannot assign attribute on non-namespace object")'
+            )
+            self.outdent()
+
         self.newline(node)
         self.visit(node.target, frame)
         self.write(" = ")
@@ -1637,17 +1660,11 @@ def visit_Name(self, node: nodes.Name, frame: Frame) -> None:
         self.write(ref)
 
     def visit_NSRef(self, node: nodes.NSRef, frame: Frame) -> None:
-        # NSRefs can only be used to store values; since they use the normal
-        # `foo.bar` notation they will be parsed as a normal attribute access
-        # when used anywhere but in a `set` context
+        # NSRef is a dotted assignment target a.b=c, but uses a[b]=c internally.
+        # visit_Assign emits code to validate that each ref is to a Namespace
+        # object only. That can't be emitted here as the ref could be in the
+        # middle of a tuple assignment.
         ref = frame.symbols.ref(node.name)
-        self.writeline(f"if not isinstance({ref}, Namespace):")
-        self.indent()
-        self.writeline(
-            "raise TemplateRuntimeError"
-            '("cannot assign attribute on non-namespace object")'
-        )
-        self.outdent()
         self.writeline(f"{ref}[{node.attr!r}]")
 
     def visit_Const(self, node: nodes.Const, frame: Frame) -> None:
diff --git a/src/jinja2/parser.py b/src/jinja2/parser.py
index 22f3f81f7..f4117754a 100644
--- a/src/jinja2/parser.py
+++ b/src/jinja2/parser.py
@@ -487,21 +487,18 @@ def parse_assign_target(
         """
         target: nodes.Expr
 
-        if with_namespace and self.stream.look().type == "dot":
-            token = self.stream.expect("name")
-            next(self.stream)  # dot
-            attr = self.stream.expect("name")
-            target = nodes.NSRef(token.value, attr.value, lineno=token.lineno)
-        elif name_only:
+        if name_only:
             token = self.stream.expect("name")
             target = nodes.Name(token.value, "store", lineno=token.lineno)
         else:
             if with_tuple:
                 target = self.parse_tuple(
-                    simplified=True, extra_end_rules=extra_end_rules
+                    simplified=True,
+                    extra_end_rules=extra_end_rules,
+                    with_namespace=with_namespace,
                 )
             else:
-                target = self.parse_primary()
+                target = self.parse_primary(with_namespace=with_namespace)
 
             target.set_ctx("store")
 
@@ -643,17 +640,25 @@ def parse_unary(self, with_filter: bool = True) -> nodes.Expr:
             node = self.parse_filter_expr(node)
         return node
 
-    def parse_primary(self) -> nodes.Expr:
+    def parse_primary(self, with_namespace: bool = False) -> nodes.Expr:
+        """Parse a name or literal value. If ``with_namespace`` is enabled, also
+        parse namespace attr refs, for use in assignments."""
         token = self.stream.current
         node: nodes.Expr
         if token.type == "name":
+            next(self.stream)
             if token.value in ("true", "false", "True", "False"):
                 node = nodes.Const(token.value in ("true", "True"), lineno=token.lineno)
             elif token.value in ("none", "None"):
                 node = nodes.Const(None, lineno=token.lineno)
+            elif with_namespace and self.stream.current.type == "dot":
+                # If namespace attributes are allowed at this point, and the next
+                # token is a dot, produce a namespace reference.
+                next(self.stream)
+                attr = self.stream.expect("name")
+                node = nodes.NSRef(token.value, attr.value, lineno=token.lineno)
             else:
                 node = nodes.Name(token.value, "load", lineno=token.lineno)
-            next(self.stream)
         elif token.type == "string":
             next(self.stream)
             buf = [token.value]
@@ -683,6 +688,7 @@ def parse_tuple(
         with_condexpr: bool = True,
         extra_end_rules: t.Optional[t.Tuple[str, ...]] = None,
         explicit_parentheses: bool = False,
+        with_namespace: bool = False,
     ) -> t.Union[nodes.Tuple, nodes.Expr]:
         """Works like `parse_expression` but if multiple expressions are
         delimited by a comma a :class:`~jinja2.nodes.Tuple` node is created.
@@ -690,8 +696,9 @@ def parse_tuple(
         if no commas where found.
 
         The default parsing mode is a full tuple.  If `simplified` is `True`
-        only names and literals are parsed.  The `no_condexpr` parameter is
-        forwarded to :meth:`parse_expression`.
+        only names and literals are parsed; ``with_namespace`` allows namespace
+        attr refs as well. The `no_condexpr` parameter is forwarded to
+        :meth:`parse_expression`.
 
         Because tuples do not require delimiters and may end in a bogus comma
         an extra hint is needed that marks the end of a tuple.  For example
@@ -704,13 +711,14 @@ def parse_tuple(
         """
         lineno = self.stream.current.lineno
         if simplified:
-            parse = self.parse_primary
-        elif with_condexpr:
-            parse = self.parse_expression
+
+            def parse() -> nodes.Expr:
+                return self.parse_primary(with_namespace=with_namespace)
+
         else:
 
             def parse() -> nodes.Expr:
-                return self.parse_expression(with_condexpr=False)
+                return self.parse_expression(with_condexpr=with_condexpr)
 
         args: t.List[nodes.Expr] = []
         is_tuple = False
diff --git a/tests/test_core_tags.py b/tests/test_core_tags.py
index 4bb95e024..2d847a2c9 100644
--- a/tests/test_core_tags.py
+++ b/tests/test_core_tags.py
@@ -538,6 +538,14 @@ def test_namespace_macro(self, env_trim):
         )
         assert tmpl.render() == "13|37"
 
+    def test_namespace_set_tuple(self, env_trim):
+        tmpl = env_trim.from_string(
+            "{% set ns = namespace(a=12, b=36) %}"
+            "{% set ns.a, ns.b = ns.a + 1, ns.b + 1 %}"
+            "{{ ns.a }}|{{ ns.b }}"
+        )
+        assert tmpl.render() == "13|37"
+
     def test_block_escaping_filtered(self):
         env = Environment(autoescape=True)
         tmpl = env.from_string(