"Our terms of service are absolutely clear on this kind of thing," the Telegraph quoted Milner, who leads Facebook's British public policy unit, as saying.
According to the paper, his comments follow the arrest last month of a man who created a Facebook group, which described the alleged murderer of two UK police constables as a 'legend'.
"Every police officer's death is a course (sic) for celebration," the group said.
Milner addressed the issue this week as Facebook made changes to the system that allows members to report concerns about postings.
A new 'Support Dashboard' will for the first time allow those who make the complaints to keep track of Facebook's response.