Terms for subject General containing went on to say that

English	Russian
he went on to say that	затем он сказал, что
he went on to say that he agreed	затем он сказал, что согласен (to give me all the details, to tell us about it, etc., и т.д.)
he went on to say that he agreed	далее он сказал, что согласен (to give me all the details, to tell us about it, etc., и т.д.)