The majority of U.S. states and territories are taking steps to reduce sexual assaults in prisons as required by federal law, according to Justice Department officials.

But seven states and one territory face a 5 percent reduction in federal grants because their governors have either refused to adopt federal standards to combat prison sexual assault as required by the Prison Rape Elimination Act, or have not committed to comply with the law, the officials said.

An estimated 4 percent of state and federal prison inmates and 3.2 percent of jail inmates reported experiencing one or more incidents of sexual victimization by another inmate or a corrections facility staff member within the past 12 months, according to the Justice Department. In addition, an estimated 9.5 percent of adjudicated youth in state juvenile facilities and state contract facilities reported sexual victimization in the past year.

“These statistics are alarming and they are unacceptable,” Deputy Attorney General James M. Cole told reporters Wednesday. “No one — and I repeat no one — should be subjected to sexual abuse while in the custody of our justice system. It serves as a violation of fundamental rights, an attack on human dignity and runs contrary to everything we stand for as a nation.”

The law to “prevent, detect and respond to” sexual abuse and rape in prisons, jails and juvenile facilities was passed unanimously by Congress and signed by President George W. Bush in 2003. May 15 was the deadline for states and territories to submit certifications or assurances of compliance to standards created by a national bipartisan commission.

The governors of Arizona, Florida, Idaho, Indiana, Nebraska, Texas and Utah as well as the Northern Mariana Islands in the Pacific either did not meet the deadline or have indicated that they do not intend to comply with the law. Texas, Florida, Idaho, Utah and Indiana all have facilities with a high rate of sexual assault by inmates or staff, according to a Bureau of Justice Statistics report.

Texas Gov. Rick Perry wrote Attorney General Eric H. Holder Jr. in April that it was “impossible” for Texas to comply with the standards because they were too costly and were a violation of states’ rights. Perry said Texas would continue the state programs it already has to reduce prison rapes.

“I’m heartened by the fact that Governor Perry recognizes that rape in prisons has to stop,” Cole said in response to a question about Perry. “I’m a bit at a loss to try and figure out why Governor Perry isn’t taking advantage of all the things that have been given to him by this statute and by the programs that we’ve put together to help achieve what he thinks is so necessary.”

Justice officials said that other governors have told them that full compliance with the prison rape elimination standards “will not be quick or easy.”

Violence and sexual assault in prison is “a culture that’s been embedded for many, many years,” said Mary Lou Leary, the principal deputy assistant attorney general of the Office of Justice Programs. “It takes time for cultures to change.”