WASHINGTON — Responding to Republicans who have repeatedly tied gun violence to mental health issues, President Obama’s new gun control plan will allow state agencies and the Social Security Administration to provide certain “protected health information” to the F.B.I. to help crack down on weapons sales to people who pose a danger to themselves or others or are unable to manage their own affairs.

The measure was part of a much broader suite of guidelines and orders to address gun violence that is plaguing the country. And while many psychiatrists and patient advocates have not objected, some groups say the plan raises red flags.

“We are concerned about the implications of this rule,” said Jennifer Mathis, a lawyer at the Bazelon Center for Mental Health Law, an advocacy group for patients. “It points a finger inappropriately at people with mental illness as a source of gun violence. It’s a bad precedent to start creating exceptions to the privacy law for people with mental illness, who are responsible for about 4 percent of incidents of gun violence.”

Virtually every push for new gun sale restrictions in recent years has been greeted by opponents countering with proposals to address mental health as a factor in gun violence.