diff --git a/Misc/NEWS b/Misc/NEWS
index 2ce06204d97..dbebc760536 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -102,6 +102,10 @@ Core and Builtins
 Library
 -------
 
+- Issue #26735: Fix :func:`os.urandom` on Solaris 11.3 and newer when reading
+  more than 1,024 bytes: call ``getrandom()`` multiple times with a limit of
+  1024 bytes per call.
+
 - Issue #16329: Add .webm to mimetypes.types_map.  Patch by Giampaolo Rodola'.
 
 - Issue #13952: Add .csv to mimetypes.types_map.  Patch by Geoff Wilson.
diff --git a/Python/random.c b/Python/random.c
index 772bfef0e87..79157b8b6f2 100644
--- a/Python/random.c
+++ b/Python/random.c
@@ -131,16 +131,23 @@ py_getrandom(void *buffer, Py_ssize_t size, int raise)
         return 0;
 
     while (0 < size) {
-        errno = 0;
+#ifdef sun
+        /* Issue #26735: On Solaris, getrandom() is limited to returning up
+           to 1024 bytes */
+        n = Py_MIN(size, 1024);
+#else
+        n = size;
+#endif
 
+        errno = 0;
 #ifdef HAVE_GETRANDOM
         if (raise) {
             Py_BEGIN_ALLOW_THREADS
-            n = getrandom(buffer, size, flags);
+            n = getrandom(buffer, n, flags);
             Py_END_ALLOW_THREADS
         }
         else {
-            n = getrandom(buffer, size, flags);
+            n = getrandom(buffer, n, flags);
         }
 #else
         /* On Linux, use the syscall() function because the GNU libc doesn't
@@ -148,11 +155,11 @@ py_getrandom(void *buffer, Py_ssize_t size, int raise)
          * https://sourceware.org/bugzilla/show_bug.cgi?id=17252 */
         if (raise) {
             Py_BEGIN_ALLOW_THREADS
-            n = syscall(SYS_getrandom, buffer, size, flags);
+            n = syscall(SYS_getrandom, buffer, n, flags);
             Py_END_ALLOW_THREADS
         }
         else {
-            n = syscall(SYS_getrandom, buffer, size, flags);
+            n = syscall(SYS_getrandom, buffer, n, flags);
         }
 #endif