Contrary to what some others have responded, I don't believe that it is necessary to read an entire work (not just a book, but even a short article) in order to cite it. A citation does not mean "I've read it"; a citation means "if you want to know where I got this idea from, or you would like more detailed information, look here". However, a comment below notes that this might only be true in some fields (I mostly publish in business, management, and information science).
That said, you are certainly responsible to cite a work responsibly, by which I mean that the work should indeed support what you are citing it to support. Without reading at least the specific sections that relate to the point related to your citation, it is impossible to be responsible in this way. For a literature review, although it is ideal to read everything that you summarize as part of your review, it is often not practical to do so, especially for reviews that evaluate a very large number of references. (This is different from a book review, which has the implicit understanding that the writer has read the entire book being reviewed, or is otherwise expected to explicitly say that they did not.) I personally consider the standard for a literature review to be what I am calling "responsible" citation: anything cited must accurately reflect what is summarized or claimed concerning the original source, which does not necessarily require reading the entire work.
For your specific situation, I suggest writing something like this: "OriginalAuthor (Year) wrote concerning ________, as summarized by BookReviewAuthor (Year)." From then on, whenever making any claims about what the book supposedly says, I would cite BookReviewAuthor, not OriginalAuthor. To me, this would be an honest way of indicating that you did not read the original book, but are rather summarizing or commenting on the book review. Of course, some readers (and reviewers) might not like the fact that you didn't read the original book, but whether that looks good or bad is secondary: it is honest. At least you're not pretending to have read a book when you only read the summary. If the readers don't like that, then they are free to read the entire book themselves (which you properly cited for their benefit). Of course, they would probably go to the book review, too, since that is easier, unless they are really, really interested.