diff --git a/examples/posix_sockets/Makefile b/examples/posix_sockets/Makefile
index b5cfaa243b..9188a0f96a 100644
--- a/examples/posix_sockets/Makefile
+++ b/examples/posix_sockets/Makefile
@@ -15,7 +15,7 @@ USEMODULE += auto_init_gnrc_netif
 USEMODULE += gnrc_ipv6_default
 USEMODULE += sock_udp
 USEMODULE += posix_sockets
-USEMODULE += posix_time
+USEMODULE += posix_sleep
 USEMODULE += posix_inet
 # Add also the shell, some shell commands
 USEMODULE += shell
diff --git a/pkg/umorse/Makefile.dep b/pkg/umorse/Makefile.dep
index 350dc2afa4..7b58f2b903 100644
--- a/pkg/umorse/Makefile.dep
+++ b/pkg/umorse/Makefile.dep
@@ -1 +1 @@
-USEMODULE += posix_time
+USEMODULE += posix_sleep
diff --git a/sys/Makefile b/sys/Makefile
index 9abc50975f..e2216b74a1 100644
--- a/sys/Makefile
+++ b/sys/Makefile
@@ -140,8 +140,8 @@ endif
 ifneq (,$(filter posix_sockets,$(USEMODULE)))
   DIRS += posix/sockets
 endif
-ifneq (,$(filter posix_time,$(USEMODULE)))
-  DIRS += posix/time
+ifneq (,$(filter posix_sleep,$(USEMODULE)))
+  DIRS += posix/sleep
 endif
 ifneq (,$(filter pthread,$(USEMODULE)))
   DIRS += posix/pthread
diff --git a/sys/Makefile.dep b/sys/Makefile.dep
index 0c02884a14..99f2b0a329 100644
--- a/sys/Makefile.dep
+++ b/sys/Makefile.dep
@@ -561,8 +561,12 @@ ifneq (,$(filter posix_semaphore,$(USEMODULE)))
   USEMODULE += posix_headers
 endif
 
-ifneq (,$(filter posix_time,$(USEMODULE)))
-  USEMODULE += xtimer
+ifneq (,$(filter posix_sleep,$(USEMODULE)))
+  USEMODULE += ztimer_msec
+  ifneq (,$(filter periph_rtt,$(USEMODULE)))
+    USEMODULE += ztimer_periph_rtt
+  endif
+  USEMODULE += ztimer_usec
   USEMODULE += posix_headers
 endif
 
diff --git a/sys/posix/time/Makefile b/sys/posix/sleep/Makefile
similarity index 62%
rename from sys/posix/time/Makefile
rename to sys/posix/sleep/Makefile
index 58c4276185..8cfde5a886 100644
--- a/sys/posix/time/Makefile
+++ b/sys/posix/sleep/Makefile
@@ -1,3 +1,3 @@
-MODULE = posix_time
+MODULE = posix_sleep
 
 include $(RIOTBASE)/Makefile.base
diff --git a/sys/posix/time/posix_time.c b/sys/posix/sleep/posix_sleep.c
similarity index 64%
rename from sys/posix/time/posix_time.c
rename to sys/posix/sleep/posix_sleep.c
index ae78095968..11581069c8 100644
--- a/sys/posix/time/posix_time.c
+++ b/sys/posix/sleep/posix_sleep.c
@@ -7,27 +7,29 @@
  */
 
 /**
- * @ingroup sys_xtimer
+ * @ingroup posix
  *
  * @{
  * @file
- * @brief xtimer posix wrapper
+ * @brief  posix sleep/usleep implementation wrapped around @ref ztimer
  * @author Kaspar Schleiser <kaspar@schleiser.de>
  * @}
  */
 
 #include <unistd.h>
 
-#include "xtimer.h"
+#include "kernel_defines.h"
+#include "timex.h"
+#include "ztimer.h"
 
 unsigned int sleep(unsigned int seconds)
 {
-    xtimer_usleep64(seconds * US_PER_SEC);
+    ztimer_sleep(ZTIMER_MSEC, seconds * MS_PER_SEC);
     return 0;
 }
 
 int usleep(useconds_t usec)
 {
-    xtimer_usleep64(usec);
+    ztimer_sleep(ZTIMER_USEC, usec);
     return 0;
 }
diff --git a/tests/posix_sleep/Makefile b/tests/posix_sleep/Makefile
new file mode 100644
index 0000000000..ff3a969bad
--- /dev/null
+++ b/tests/posix_sleep/Makefile
@@ -0,0 +1,9 @@
+include ../Makefile.tests_common
+
+USEMODULE += posix_sleep
+
+# Pull-in periph-rtt on board that provides this feature to switch to the RTT
+# backend of ztimer
+FEATURES_OPTIONAL += periph_rtt
+
+include $(RIOTBASE)/Makefile.include
diff --git a/tests/posix_sleep/Makefile.ci b/tests/posix_sleep/Makefile.ci
new file mode 100644
index 0000000000..b9ff275375
--- /dev/null
+++ b/tests/posix_sleep/Makefile.ci
@@ -0,0 +1,3 @@
+BOARD_INSUFFICIENT_MEMORY := \
+    nucleo-l011k4 \
+    #
diff --git a/tests/posix_time/README.md b/tests/posix_sleep/README.md
similarity index 88%
rename from tests/posix_time/README.md
rename to tests/posix_sleep/README.md
index e8d161db4a..b9b6f89853 100644
--- a/tests/posix_time/README.md
+++ b/tests/posix_sleep/README.md
@@ -1,4 +1,4 @@
-# posix_time test application
+# posix_sleep test application
 
 This test tests POSIX' `sleep()` and `usleep()`.
 The test script also checks the sanity of the timings by comparing the overall
diff --git a/tests/posix_time/main.c b/tests/posix_sleep/main.c
similarity index 100%
rename from tests/posix_time/main.c
rename to tests/posix_sleep/main.c
diff --git a/tests/posix_time/tests/01-run.py b/tests/posix_sleep/tests/01-run.py
similarity index 100%
rename from tests/posix_time/tests/01-run.py
rename to tests/posix_sleep/tests/01-run.py
diff --git a/tests/posix_time/Makefile b/tests/posix_time/Makefile
deleted file mode 100644
index 65e58f6d25..0000000000
--- a/tests/posix_time/Makefile
+++ /dev/null
@@ -1,5 +0,0 @@
-include ../Makefile.tests_common
-
-USEMODULE += posix_time
-
-include $(RIOTBASE)/Makefile.include