The governor also announced that tribal officials are organizing a memorial service for 2 p.m. on Tuesday on the Minnesota Capitol grounds.
Ten people -- including the teenage gunman, five classmates, one teacher and one security guard died at the Red Lake High School; and the suspect also shot his grandparents before going to school, press reports said.
Relatives told a Minnesota newspaper that the shooting suspect's father committed suicide several years ago and that his mother was in a nursing home because of serious injuries suffered in a car wreck.
The suspect is described in various press reports as a loner who dressed in black. He reportedly talked about shooting up the school last year. Witnesses said he appeared to enjoy shooting his classmates on Monday, and some reports suggested he was imitating the Columbine High School killers.
He reportedly was armed with two pistols and a shotgun, and he turned one of the guns on himself as police moved in.
The Brady Campaign to Prevent Handgun Violence United with the Million Mom March said the shooting should be a wake-up call to federal lawmakers.
"Our leaders are preaching about the culture of life. They should spend the same amount of energy taking steps to stop our nation's culture of death," said Brady Campaign President Michael Barnes.
The gun control group said the teen's attack on his school cannot be viewed as an isolated incident.
"In recent months, we have seen horrible shooting attacks in shopping malls, office buildings, courthouses, the homes of judges, private hunting lands and it seems like every other kind of place we like to believe is safe," Barnes said.
In its press release, the Brady campaign criticized federal lawmakers for letting the "assault weapons ban" expire.
The Brady Campaign also complained about "limited law enforcement investigations of gun sellers"; laws mandating the immediate destruction of gun-sale records; and a pending bill that would "make it impossible for victims of gun violence to seek justice against reckless gun sellers in the courts." (That pending legislation is intended to shield gun makers from groups that want to bankrupt them.)
"We need to do more to make sure our communities -- and especially our young people -- are safe from gun violence," said Kate Havelin, president of the Twin Cities, Minnesota Million Mom March chapter.
"Today I hope all of us think of those who died, those who were injured, and all of those whose lives have been changed because of gun violence."
Sarah Brady, chair of the Brady Campaign, wondered when the nation's leaders will have had enough: "When will the government do something to help stop the bloodshed?" she asked.
In April 1999, after the Columbine High School shooting, then-President Bill Clinton, a gun control supporter, suggested there was only so much that government could do.
He said parents should take time to ask themselves "what else they can do to shield our children from violent images and experiences that warp young perceptions and obscure the consequences of violence."
