1. E Vasilenko and E Lamm Learning to Read Russian (Russky Yazyk, Moscow, 1986 and other years) 440pp
(WARNING: DO NOT confuse this with the same authors' similar sounding Russian on your own: Learning to read Russian 308pp)
You can find copies of this on the usual internet bookshop aggregation sites This is a Soviet era self-instructional course. Although completely focused on acquiring skills in reading the language, there are accompanying tapes (which I have uploaded to archive.org) which are used early on to teach pronunciation.
Unlike the Soviet texts of an earlier period, which were printed on poor quality paper and looked very dull, this is in a different class altogether: printed on glossy paper with plenty of colour photographs, drawings, cartoons, crosswords, it is a an attractive and enjoyable text. Divided into 40 Chapters distributed amongst 7 Units. Unit I is devoted to teaching the alphabet, script, pronunciation and basic sentence structure. The succeeding Units develop the grammar, with plenty of exercises, and practice texts of increasing length and sophistication. There are answers to some exercises given at the back of the book, together with physical and political maps of the USSR, together with a 2,500 word Russian-English vocabulary.
I'm not professionally equipped to evaluate the level properly, but I guess it takes you to about B1-B2 on the CEFR levels.
2. Patricia M. Arant Russian for Reading (Slavica Publishers, Columbus Ohio, 1981) 214pp
This is the only other textbook purely for learning to read Russian that I am aware of. Designed for classroom use, rather tha self-instruction, it is a much more spartan product than the Soviet text. Alphabet, script, pronunciation etc are dealt with in a brisk 12 page Introduction, which sets the pace for the rest of the book. Twelve lessons, 800 word vocabulary. A useful supplement to the above, but difficult to use as a self-instruction text.