The policy calls for fraternities to have security at doors, guard their stairs, have keys to each room, sober brothers at parties and to eliminate pre-mixed drinks.
In November, the university suspended all fraternities and associated parties until this month after a Rolling Stone magazine article about the student's claims.
Despite scrutiny of the article's depiction of the alleged rape of a then-UVA freshman, identified in the article as Jackie, the university stuck to its promise to review how sexual assault is handled and to make Greek life safer.
UVA gave its fraternity members until Friday to sign the agreement if they wanted to have the suspension lifted. But Alpha Tau Omega and Kappa Alpha Order released statements on their national fraternity letterhead saying they would not do so.
They said the university unfairly punished members of Greek life when it uniformly suspended social activities two days after the Rolling Stone article was published, and said they are concerned the demands will create new liability and "set a dangerous precedent of an erosion of student and organizational rights."
Instead, both fraternities plan to ignore the new rules set by UVA and resume activities.
The university said the rules were developed by student groups and said it won't comment until after the Friday deadline for fraternities to sign the agreement has passed.
A source familiar with the thinking of the national fraternities said this could result in litigation if UVA tries to limit the fraternities that won't sign the new agreement.
The Washington Post reports that Phi Kappa Psi is one of the fraternities that signed the agreement and remains committed to improving safety during events. Jackie told Rolling Stone that she was assaulted by seven men at a Phi Kappa Psi party.
In the weeks that followed the article, the Washington Post and other news organizations began scrutinizing the details of Jackie's story. CNN spoke to Jackie's friends
, who told a different version of events from that night, and Phi Kappa Psi produced records that seemed to dispute what she said happened.
Charlottesville Police investigated after the story was printed, and said earlier this week that police found no "substantive basis to confirm that the allegations raised in the Rolling Stone article occurred at Phi Kappa Psi."
Police have not said whether they believe Jackie was raped.
Rolling Stone apologized and launched an investigation of its own. The magazine editor acknowledged that the writer never contacted some of the witnesses or any of the accused.