The couple announced they had split in May, and Schwarzenegger later disclosed he had fathered a child with a member of his household staff.
The actor and former California governor filed his response to Shriver's divorce petition Wednesday in Los Angeles.
The issues of whether Shriver will receive spousal support and who will pay her attorney's fees are the only differences in their initial filings to end their 25-year marriage.
They are seeking joint custody of two of their sons, who are 17 and 13.
Shriver filed for divorce on July 1.