CREATE TABLE `test` (
  `cnt` int(11) NOT NULL AUTO_INCREMENT,
  `a` int(11) DEFAULT NULL,
  `b` int(11) DEFAULT NULL,
  PRIMARY KEY (`cnt`)
)

CREATE TABLE `test_current` (
  `a` int(11) DEFAULT NULL,
  `b` int(11) DEFAULT NULL
)

mysql> insert into test_current (a,b) values (1,1),(2,2);
Query OK, 2 rows affected (0.00 sec)
Records: 2  Duplicates: 0  Warnings: 0

mysql> INSERT INTO test (a,b) SELECT a,b FROM test_current;
Query OK, 2 rows affected, 1 warning (0.00 sec)
Records: 2  Duplicates: 0  Warnings: 1

mysql> select * from test;
+-----+------+------+
| cnt | a    | b    |
+-----+------+------+
|   1 |    1 |    1 |
|   2 |    2 |    2 |
+-----+------+------+
2 rows in set (0.00 sec)

mysql> INSERT INTO test (a,b) SELECT a,b FROM test_current;
Query OK, 2 rows affected, 1 warning (0.00 sec)
Records: 2  Duplicates: 0  Warnings: 1

mysql> select * from test;
+-----+------+------+
| cnt | a    | b    |
+-----+------+------+
|   1 |    1 |    1 |
|   2 |    2 |    2 |
|   4 |    1 |    1 |
|   5 |    2 |    2 |
+-----+------+------+

ALTER TABLE `test` AUTO_INCREMENT = 1;
INSERT INTO test (a,b) SELECT a,b FROM test_current;

innodb_autoinc_lock_mode=0