It depends on the semantic of the primary key. If it's just autoincrement, then use something like:
insert into table1 (all columns except pk)
select all_columns_except_pk
from table2;
If PK means something, you need to find a way to determine which record should have priority. You could create a select query to find duplicates first (see answer by cpitis). Then eliminate the ones you don't want to keep and use the above insert to add records that remain.
They have a clever script to use the information_schema tables to get the "id" columns:
SET @db:='id_new';
select @max_id:=max(AUTO_INCREMENT) from information_schema.tables;
select concat('update ',table_name,' set ', column_name,' = ',column_name,'+',@max_id,' ; ') from information_schema.columns where table_schema=@db and column_name like '%id' into outfile 'update_ids.sql';
use id_new
source update_ids.sql;