Perhaps you could create an indexing table which provides a sequential key relating to the key in your target table. Then you can join this indexing table to your target table and use a where clause to more efficiently get the rows you want.
#create table to store sequences
CREATE TABLE seq (
seq_no int not null auto_increment,
id int not null,
primary key(seq_no),
unique(id)
);
#create the sequence
TRUNCATE seq;
INSERT INTO seq (id) SELECT id FROM mytable ORDER BY id;
#now get 1000 rows from offset 1000000
SELECT mytable.*
FROM mytable
INNER JOIN seq USING(id)
WHERE seq.seq_no BETWEEN 1000000 AND 1000999;