HONOLULU — President Obama announced two new executive actions on Friday that nudge his gun control agenda forward by making it easier for states to provide information about people with mental illness to the federal background check system.

Last year, Mr. Obama failed to win support in Congress for tougher background checks for gun purchases and new limits on assault weapons. The president had made both changes top legislative priorities after the shootings at the elementary school in Newtown, Conn.

After the legislation failed, Mr. Obama vowed to take whatever steps his administration could through executive action. He later issued 25 executive orders intended to tighten the rules for gun ownership.

Among the orders that Mr. Obama already signed are efforts to include more information about mental illness in the federal background check system, new efforts to research the causes of gun violence, incentives for schools to hire more security officers, and new requirements for federal authorities to trace guns used in crimes.

In the latest executive actions, the Department of Justice is proposing to clarify that the term “committed to a mental institution” includes involuntary outpatient as well as inpatient commitments.

The clarification would help states determine what information should be made accessible to the federal background check system.

The Department of Health and Human Services relaxed some privacy protections to help identify in the background check system those people who, under federal law, should be prohibited from owning a gun for mental health reasons. A recent investigation by the New York Times showed how powerless law enforcement can be when it comes to keeping guns out of the hands of the mentally ill.

The department proposed a rule to give certain entities covered by the Health Insurance Portability and Accountability Act permission to submit to the background check system the “limited” information required to prevent people with mental illness from obtaining firearms.

“Too many Americans have been severely injured or lost their lives as a result of gun violence,” the White House said in an email statement.

“While the vast majority of Americans who experience a mental illness are not violent, in some cases when persons with a mental illness do not receive the treatment they need the result can be tragedies such as homicide or suicide.”

The White House added, “The federal background check system is the most effective way to assure that such individuals are not able to purchase a firearm from a licensed gun dealer.”

Michael D. Shear contributed reporting from Washington.