(CNN) - Six people were killed and 12 others wounded -- including U.S. Rep. Gabrielle Giffords -- in a shooting outside a Tucson, Arizona, grocery store where the congresswoman was holding a constituent meeting, police said.
The suspect in the shooting was in custody, according to U.S. Capitol Police, who did not identify the alleged gunman.
Darci Slaten, a spokeswoman for University Medical Center in Tucson, said Giffords, 40, was undergoing surgery Saturday afternoon for a gunshot wound to the head.
Local law enforcement officials have not provided a public accounting of the injuries, but President Obama called the shooting an "unspeakable tragedy," and said "some have passed away," according to a statement from the White House. He said Giffords was "gravely wounded."
A federal judge from Arizona was among the victims, though the judge's condition was unknown, a law enforcement source told CNN.
The shooting happened shortly after 10 a.m. MST at a Safeway grocery store, Pima County Sheriff's Department spokesman Jason Ogan said.
Giffords, 40, was holding a constituent meeting at the store when the shooting occurred, according to a schedule posted on her website.
An FBI spokesman said the agency was sending agents to the scene, and two senior Obama administration officials said the White House is monitoring the situation. They said they believed that a congressional staffer may have been killed.
Pictures from the scene showed a Giffords banner hanging from the storefront.
At least two victims with gunshot wounds were transported at Northwest Medical Center, according to spokesman Richard Parker.
The motive for the shooting is unclear, Ogan said.
"We're just trying to sort this out right now," he said.
An employee of a nearby business, Jason Pekau, told CNN that he did not see the shooting, but heard "15 to 20 gunshots."
Giffords, a Democrat, was first elected in 2006. She has served as chairwoman of the House Space and Aeronautics Subcommittee and also holds seats on the House Science and Technology and Armed Services committees.
She won her third term in a closely contested race against a Tea Party-sponsored candidate and was one of three Democratic legislators who reported vandalism at their offices following the March vote on health care reform.
She is married to Navy Capt. Mark Kelly, a NASA astronaut who is scheduled to lead a space shuttle mission to the International Space Station.
Obama said information about the shooting was continuing to flow in.
"We do not yet have all the answers," he said. What we do know is that such a senseless and terrible act of violence has no place in a free society."
House Speaker John Boehner said he was "horrified" by the shooting.
"An attack on one who serves is an attack on all who serve," he said. "Acts and threats of violence against public officials have no place in our society."
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