diff --git a/src/sage/combinat/set_partition.py b/src/sage/combinat/set_partition.py
index a820cd9bd69..e9d78b853ea 100644
--- a/src/sage/combinat/set_partition.py
+++ b/src/sage/combinat/set_partition.py
@@ -2034,6 +2034,14 @@ class SetPartitions(UniqueRepresentation, Parent):
         sage: SetPartitions('aabcd').cardinality()                                      # needs sage.libs.flint
         15
 
+    If the number of parts exceeds the length of the set,
+    an empty iterator is returned (:issue:`37643`)::
+
+        sage: SetPartitions(range(3), 4).list()
+        []
+        sage: SetPartitions('abcd', 6).list()
+        []
+
     REFERENCES:
 
     - :wikipedia:`Partition_of_a_set`
@@ -2062,18 +2070,16 @@ def __classcall_private__(cls, s=None, part=None):
                 pass
             s = frozenset(s)
 
-        if part is not None:
+        if part is None:
+            return SetPartitions_set(s)
+        else:
             if isinstance(part, (int, Integer)):
-                if len(s) < part:
-                    raise ValueError("part must be <= len(set)")
                 return SetPartitions_setn(s, part)
             else:
                 part = sorted(part, reverse=True)
                 if part not in Partitions(len(s)):
                     raise ValueError("part must be an integer partition of %s" % len(s))
                 return SetPartitions_setparts(s, Partition(part))
-        else:
-            return SetPartitions_set(s)
 
     def __contains__(self, x):
         """
diff --git a/src/sage/combinat/set_partition_iterator.pyx b/src/sage/combinat/set_partition_iterator.pyx
index 66d2d829acc..93024e7666a 100644
--- a/src/sage/combinat/set_partition_iterator.pyx
+++ b/src/sage/combinat/set_partition_iterator.pyx
@@ -130,5 +130,7 @@ def set_partition_iterator_blocks(base_set, Py_ssize_t k):
     cdef Py_ssize_t n = len(base)
     cdef list a = list(range(n))
     # TODO: implement _set_partition_block_gen as an iterative algorithm
+    if n < k:
+        return
     for P in _set_partition_block_gen(n, k, a):
         yield from_word(<list> P, base)