The two actors - who played Hikaru Sulu and Captain Kirk in the original 1960s sci fi television series set aboard the Starship Enterprise - have been locked in an ongoing feud for many years.
Takei, 85, told The Guardian: "I know he came to London to promote his book and talked about me wanting publicity by using his name. So I decided I don’t need his name to get publicity. I have much more substantial subject matter that I want to get publicity for, so I’m not going to refer to Bill in this interview at all.
He added: “Although I just did. He’s just a cantankerous old man and I’m going to leave him to his devices. I’m not going to play his game.”
Shatner, 91, recently told The Times he had had enough of his former Star Trek co-star making public comments about how difficult he had been to work with.
He said: “I began to understand that they were doing it for publicity. Sixty years after some incident they are still on that track. Don’t you think that’s a little weird? It’s like a sickness. George has never stopped blackening my name. These people are bitter and embittered. I have run out of patience with them. Why give credence to people consumed by envy and hate?”
Takei has often spoken about how he found Shatner a "prima donna" to work with.
Shatner's relationship with Leonard Nimoy, who played Spock, became strained in the years leading up to his death in 2015.
And in Shatner's new book - Boldly Go, Reflections on a Life of Awe and Wonder - he tells how Nichelle Nichols, who played Uhura, told him his co-stars found him “cold and arrogant”.
Shatner wrote: “I was horrified to learn this, ashamed that I hadn’t realised it."
Takei said of the Star Trek cast: “Except for one, who was a prima donna... the rest of us shared a great camaraderie."
Watch: William Shatner discusses growing older