diff --git a/src/backend/utils/adt/datetime.c b/src/backend/utils/adt/datetime.c
index 1b86fff2fb..7abdc62f41 100644
--- a/src/backend/utils/adt/datetime.c
+++ b/src/backend/utils/adt/datetime.c
@@ -1970,6 +1970,17 @@ DecodeTimeOnly(char **field, int *ftype, int nf,
 				break;
 
 			case DTK_TIME:
+
+				/*
+				 * This might be an ISO time following a "t" field.
+				 */
+				if (ptype != 0)
+				{
+					if (ptype != DTK_TIME)
+						return DTERR_BAD_FORMAT;
+					ptype = 0;
+				}
+
 				dterr = DecodeTime(field[i], (fmask | DTK_DATE_M),
 								   INTERVAL_FULL_RANGE,
 								   &tmask, tm, fsec);
diff --git a/src/test/regress/expected/horology.out b/src/test/regress/expected/horology.out
index 195fe72644..241713cc51 100644
--- a/src/test/regress/expected/horology.out
+++ b/src/test/regress/expected/horology.out
@@ -274,6 +274,161 @@ SELECT time with time zone 'J2452271 T040506.789 America/Los_Angeles';
  04:05:06.789-08
 (1 row)
 
+-- Check time formats required by ISO 8601
+SELECT time without time zone '040506.07';
+    time     
+-------------
+ 04:05:06.07
+(1 row)
+
+SELECT time without time zone '04:05:06.07';
+    time     
+-------------
+ 04:05:06.07
+(1 row)
+
+SELECT time without time zone '040506';
+   time   
+----------
+ 04:05:06
+(1 row)
+
+SELECT time without time zone '04:05:06';
+   time   
+----------
+ 04:05:06
+(1 row)
+
+SELECT time without time zone '0405';
+   time   
+----------
+ 04:05:00
+(1 row)
+
+SELECT time without time zone '04:05';
+   time   
+----------
+ 04:05:00
+(1 row)
+
+SELECT time without time zone 'T040506.07';
+    time     
+-------------
+ 04:05:06.07
+(1 row)
+
+SELECT time without time zone 'T04:05:06.07';
+    time     
+-------------
+ 04:05:06.07
+(1 row)
+
+SELECT time without time zone 'T040506';
+   time   
+----------
+ 04:05:06
+(1 row)
+
+SELECT time without time zone 'T04:05:06';
+   time   
+----------
+ 04:05:06
+(1 row)
+
+SELECT time without time zone 'T0405';
+   time   
+----------
+ 04:05:00
+(1 row)
+
+SELECT time without time zone 'T04:05';
+   time   
+----------
+ 04:05:00
+(1 row)
+
+-- 8601 says "Thh" is allowed, but we intentionally reject it as too vague
+SELECT time without time zone 'T04';
+ERROR:  invalid input syntax for type time: "T04"
+LINE 1: SELECT time without time zone 'T04';
+                                      ^
+SELECT time with time zone '040506.07+08';
+     timetz     
+----------------
+ 04:05:06.07+08
+(1 row)
+
+SELECT time with time zone '04:05:06.07+08';
+     timetz     
+----------------
+ 04:05:06.07+08
+(1 row)
+
+SELECT time with time zone '040506+08';
+   timetz    
+-------------
+ 04:05:06+08
+(1 row)
+
+SELECT time with time zone '04:05:06+08';
+   timetz    
+-------------
+ 04:05:06+08
+(1 row)
+
+SELECT time with time zone '0405+08';
+   timetz    
+-------------
+ 04:05:00+08
+(1 row)
+
+SELECT time with time zone '04:05+08';
+   timetz    
+-------------
+ 04:05:00+08
+(1 row)
+
+SELECT time with time zone 'T040506.07+08';
+     timetz     
+----------------
+ 04:05:06.07+08
+(1 row)
+
+SELECT time with time zone 'T04:05:06.07+08';
+     timetz     
+----------------
+ 04:05:06.07+08
+(1 row)
+
+SELECT time with time zone 'T040506+08';
+   timetz    
+-------------
+ 04:05:06+08
+(1 row)
+
+SELECT time with time zone 'T04:05:06+08';
+   timetz    
+-------------
+ 04:05:06+08
+(1 row)
+
+SELECT time with time zone 'T0405+08';
+   timetz    
+-------------
+ 04:05:00+08
+(1 row)
+
+SELECT time with time zone 'T04:05+08';
+   timetz    
+-------------
+ 04:05:00+08
+(1 row)
+
+-- 8601 says "Thh" is allowed, but we intentionally reject it as too vague
+SELECT time with time zone 'T04+08';
+ERROR:  invalid input syntax for type time with time zone: "T04+08"
+LINE 1: SELECT time with time zone 'T04+08';
+                                   ^
 SET DateStyle = 'Postgres, MDY';
 -- Check Julian dates BC
 SELECT date 'J1520447' AS "Confucius' Birthday";
diff --git a/src/test/regress/sql/horology.sql b/src/test/regress/sql/horology.sql
index 2aa4a49b3f..e5cf12ff63 100644
--- a/src/test/regress/sql/horology.sql
+++ b/src/test/regress/sql/horology.sql
@@ -59,6 +59,35 @@ SELECT time with time zone 'T040506.789 -08';
 SELECT time with time zone 'T040506.789 America/Los_Angeles';
 SELECT time with time zone '2001-12-27 T040506.789 America/Los_Angeles';
 SELECT time with time zone 'J2452271 T040506.789 America/Los_Angeles';
+-- Check time formats required by ISO 8601
+SELECT time without time zone '040506.07';
+SELECT time without time zone '04:05:06.07';
+SELECT time without time zone '040506';
+SELECT time without time zone '04:05:06';
+SELECT time without time zone '0405';
+SELECT time without time zone '04:05';
+SELECT time without time zone 'T040506.07';
+SELECT time without time zone 'T04:05:06.07';
+SELECT time without time zone 'T040506';
+SELECT time without time zone 'T04:05:06';
+SELECT time without time zone 'T0405';
+SELECT time without time zone 'T04:05';
+-- 8601 says "Thh" is allowed, but we intentionally reject it as too vague
+SELECT time without time zone 'T04';
+SELECT time with time zone '040506.07+08';
+SELECT time with time zone '04:05:06.07+08';
+SELECT time with time zone '040506+08';
+SELECT time with time zone '04:05:06+08';
+SELECT time with time zone '0405+08';
+SELECT time with time zone '04:05+08';
+SELECT time with time zone 'T040506.07+08';
+SELECT time with time zone 'T04:05:06.07+08';
+SELECT time with time zone 'T040506+08';
+SELECT time with time zone 'T04:05:06+08';
+SELECT time with time zone 'T0405+08';
+SELECT time with time zone 'T04:05+08';
+-- 8601 says "Thh" is allowed, but we intentionally reject it as too vague
+SELECT time with time zone 'T04+08';
 SET DateStyle = 'Postgres, MDY';
 -- Check Julian dates BC
 SELECT date 'J1520447' AS "Confucius' Birthday";