CHICAGO  Facing criticism that physical evidence from sexual assault cases in Illinois often went unanalyzed, Gov. Patrick J. Quinn this week signed a law requiring the police to test all rape kits. State officials and victims’ advocates said it is the first such law in the nation.

Over the past year, critics had exposed a backlog of thousands of untested rape kits in Illinois, and officials said the law would send an important message.

“As a direct result of this law, we will increase the number of arrests and prosecutions of sex offenders and get them out of our communities and into prison,” said Lisa Madigan, the state’s attorney general.

On Wednesday, Human Rights Watch released a report showing that since 1995, only about 20 percent of rape kits, which contain physical evidence obtained from victims, could be confirmed as having been tested in Illinois. More than 4,000 kits had gone untested, the report found.