diff --git a/src/Functions/date_trunc.cpp b/src/Functions/date_trunc.cpp
index dd3ea0b877b..7b094174047 100644
--- a/src/Functions/date_trunc.cpp
+++ b/src/Functions/date_trunc.cpp
@@ -2,6 +2,7 @@
 #include <Columns/ColumnString.h>
 #include <Columns/ColumnsNumber.h>
 #include <DataTypes/DataTypeDate.h>
+#include <DataTypes/DataTypeDate32.h>
 #include <DataTypes/DataTypeDateTime.h>
 #include <DataTypes/DataTypeInterval.h>
 #include <Formats/FormatSettings.h>
@@ -43,6 +44,7 @@ public:
         enum ResultType
         {
             Date,
+            Date32,
             DateTime,
             DateTime64,
         };
@@ -75,11 +77,11 @@ public:
 
         bool second_argument_is_date = false;
         auto check_second_argument = [&] {
-            if (!isDate(arguments[1].type) && !isDateTime(arguments[1].type) && !isDateTime64(arguments[1].type))
+            if (!isDateOrDate32(arguments[1].type) && !isDateTime(arguments[1].type) && !isDateTime64(arguments[1].type))
                 throw Exception(ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT, "Illegal type {} of 2nd argument of function {}. "
                     "Should be a date or a date with time", arguments[1].type->getName(), getName());
 
-            second_argument_is_date = isDate(arguments[1].type);
+            second_argument_is_date = isDateOrDate32(arguments[1].type);
 
             if (second_argument_is_date && ((datepart_kind == IntervalKind::Kind::Hour)
                 || (datepart_kind == IntervalKind::Kind::Minute) || (datepart_kind == IntervalKind::Kind::Second)))
@@ -119,6 +121,8 @@ public:
 
         if (result_type == ResultType::Date)
             return std::make_shared<DataTypeDate>();
+        if (result_type == ResultType::Date32)
+            return std::make_shared<DataTypeDate32>();
         else if (result_type == ResultType::DateTime)
             return std::make_shared<DataTypeDateTime>(extractTimeZoneNameFromFunctionArguments(arguments, 2, 1, false));
         else
diff --git a/src/Functions/toStartOfInterval.cpp b/src/Functions/toStartOfInterval.cpp
index 21b7cf895d2..35fb43df131 100644
--- a/src/Functions/toStartOfInterval.cpp
+++ b/src/Functions/toStartOfInterval.cpp
@@ -44,9 +44,9 @@ public:
         auto check_first_argument = [&]
         {
             const DataTypePtr & type_arg1 = arguments[0].type;
-            if (!isDate(type_arg1) && !isDateTime(type_arg1) && !isDateTime64(type_arg1))
+            if (!isDateOrDate32(type_arg1) && !isDateTime(type_arg1) && !isDateTime64(type_arg1))
                 throw Exception(ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT,
-                    "Illegal type {} of 1st argument of function {}, expected a Date, DateTime or DateTime64",
+                    "Illegal type {} of 1st argument of function {}, expected a Date, Date32, DateTime or DateTime64",
                     type_arg1->getName(), getName());
             value_is_date = isDate(type_arg1);
         };
@@ -56,6 +56,7 @@ public:
         enum class ResultType : uint8_t
         {
             Date,
+            Date32,
             DateTime,
             DateTime64
         };
@@ -128,6 +129,8 @@ public:
         {
             case ResultType::Date:
                 return std::make_shared<DataTypeDate>();
+            case ResultType::Date32:
+                return std::make_shared<DataTypeDate32>();
             case ResultType::DateTime:
                 return std::make_shared<DataTypeDateTime>(extractTimeZoneNameFromFunctionArguments(arguments, 2, 0, false));
             case ResultType::DateTime64:
@@ -185,6 +188,12 @@ private:
             if (time_column_vec)
                 return dispatchForIntervalColumn(assert_cast<const DataTypeDate &>(time_column_type), *time_column_vec, interval_column, result_type, time_zone, input_rows_count);
         }
+        else if (isDate32(time_column_type))
+        {
+            const auto * time_column_vec = checkAndGetColumn<ColumnDate32>(&time_column_col);
+            if (time_column_vec)
+                return dispatchForIntervalColumn(assert_cast<const DataTypeDate32 &>(time_column_type), *time_column_vec, interval_column, result_type, time_zone, input_rows_count);
+        }
         throw Exception(ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT, "Illegal column for 1st argument of function {}, expected a Date, DateTime or DateTime64", getName());
     }
 
diff --git a/tests/queries/0_stateless/00403_to_start_of_day.reference b/tests/queries/0_stateless/00403_to_start_of_day.reference
index d00491fd7e5..1c96b0ed64f 100644
--- a/tests/queries/0_stateless/00403_to_start_of_day.reference
+++ b/tests/queries/0_stateless/00403_to_start_of_day.reference
@@ -1 +1,2 @@
 1
+2024-08-26 00:00:00
diff --git a/tests/queries/0_stateless/00403_to_start_of_day.sql b/tests/queries/0_stateless/00403_to_start_of_day.sql
index e298afd80ba..2dfcfccec38 100644
--- a/tests/queries/0_stateless/00403_to_start_of_day.sql
+++ b/tests/queries/0_stateless/00403_to_start_of_day.sql
@@ -1 +1,2 @@
 SELECT toStartOfDay(now()) = toDateTime(toDate(now()));
+SELECT toStartOfDay(toDate32(now()));
diff --git a/tests/queries/0_stateless/02935_date_trunc_case_unsensitiveness.reference b/tests/queries/0_stateless/02935_date_trunc_case_unsensitiveness.reference
index 70a26e5447d..066ca3cfd55 100644
--- a/tests/queries/0_stateless/02935_date_trunc_case_unsensitiveness.reference
+++ b/tests/queries/0_stateless/02935_date_trunc_case_unsensitiveness.reference
@@ -1,11 +1,16 @@
 2022-03-01 00:00:00
 2022-03-01
 2022-02-28
+2022-02-28
 2022-03-01 00:00:00
 2022-03-01
 2022-02-28
+2022-02-28
 2022-03-01 00:00:00
 2022-03-01
+2022-03-01 00:00:00
+2022-03-01
+2022-02-28
 2022-02-28
 2022-03-01 12:12:12.012000000
 2022-03-01 12:12:12.012346
diff --git a/tests/queries/0_stateless/02935_date_trunc_case_unsensitiveness.sql b/tests/queries/0_stateless/02935_date_trunc_case_unsensitiveness.sql
index df290f3deac..2e8e6dcd093 100644
--- a/tests/queries/0_stateless/02935_date_trunc_case_unsensitiveness.sql
+++ b/tests/queries/0_stateless/02935_date_trunc_case_unsensitiveness.sql
@@ -1,12 +1,17 @@
 SELECT dateTrunc('DAY', toDateTime('2022-03-01 12:55:55'));
 SELECT dateTrunc('MONTH', toDateTime64('2022-03-01 12:55:55', 2));
 SELECT dateTrunc('WEEK', toDate('2022-03-01'));
+SELECT dateTrunc('WEEK', toDate32('2022-03-01'));
 SELECT dateTrunc('Day', toDateTime('2022-03-01 12:55:55'));
 SELECT dateTrunc('Month', toDateTime64('2022-03-01 12:55:55', 2));
 SELECT dateTrunc('Week', toDate('2022-03-01'));
+SELECT dateTrunc('Week', toDate32('2022-03-01'));
 SELECT dateTrunc('day', toDateTime('2022-03-01 12:55:55'));
 SELECT dateTrunc('month', toDateTime64('2022-03-01 12:55:55', 2));
+SELECT dateTrunc('day', toDate32('2022-03-01'));
+SELECT dateTrunc('month', toDate32('2022-03-01'));
 SELECT dateTrunc('week', toDate('2022-03-01'));
+SELECT dateTrunc('week', toDate32('2022-03-01'));
 SELECT dateTrunc('Nanosecond', toDateTime64('2022-03-01 12:12:12.0123', 3));
 SELECT dateTrunc('MicroSecond', toDateTime64('2022-03-01 12:12:12.0123456', 7));
 SELECT dateTrunc('MILLISECOND', toDateTime64('2022-03-01 12:12:12.012324251', 9));
@@ -25,3 +30,6 @@ SELECT dateTrunc('MILLISECOND', toDateTime('2022-03-01')); -- {  serverError ILL
 SELECT dateTrunc('Nanosecond', toDate('2022-03-01')); -- {  serverError ILLEGAL_TYPE_OF_ARGUMENT }
 SELECT dateTrunc('MicroSecond', toDate('2022-03-01')); -- {  serverError ILLEGAL_TYPE_OF_ARGUMENT }
 SELECT dateTrunc('MILLISECOND', toDate('2022-03-01')); -- {  serverError ILLEGAL_TYPE_OF_ARGUMENT }
+SELECT dateTrunc('Nanosecond', toDate32('2022-03-01')); -- {  serverError ILLEGAL_TYPE_OF_ARGUMENT }
+SELECT dateTrunc('MicroSecond', toDate32('2022-03-01')); -- {  serverError ILLEGAL_TYPE_OF_ARGUMENT }
+SELECT dateTrunc('MILLISECOND', toDate32('2022-03-01')); -- {  serverError ILLEGAL_TYPE_OF_ARGUMENT }