Update at 5:45 p.m. ET

House Minority Leader Nancy Pelosi praised Giffords just now at an event in the San Francisco Bay Area.

The California Democrat saluted the commitment of Giffords and her husband, Navy Capt. Mark Kelly, an astronaut, to public service. Giffords "is a strong fighter," Pelosi said. "The news has improved (about Giffords' condition). ...We're all very prayerful."

Pelosi and Democrats Barbara Lee and John Garamendi led the audience in a moment of silence. At least five people died in the shooting, according to the Associated Press. Giffords is out of surgery and doctors in Arizona are optimistic about her chances for recovery.

Update at 5:31 p.m. ET

We have been following news about Rep. Gabrielle Giffords, a Democrat, who was shot in the head earlier today while meeting with constituents outside of a grocery store in Tucson, Ariz.

U.S. District Judge John Roll and a 9-year-old girl were killed in the shooting, which left several others wounded. To see a USA TODAY photo gallery of today's events, please click on the link.

U.S. Attorney General Eric Holder said the FBI is working with law enforcement officials in Arizona on the investigation. Federal prosecutors and law enforcement have been directed by Holder to "use every resource necessary" in the investigation.

Update at 5 p.m. ET

Arizona Gov. Jan Brewer is speaking. "I am just heartbroken. Gabby is more than a colleague. She is a friend."

Brewer, a Republican, and Giffords, a Democrat, served together in the Arizona Legislature. "She never played partisan politics ... always concerned about what's best for her district. ...She is a gracious public servant," Brewer said.

Brewer called this "senseless and cruel violence" and has ordered all state flags to be flown at half staff in honor of the five people who have died in the Tucson shooting. "This is an unbelievable tragedy that the people of Arizona experienced today," she said. "One of our worst nightmares."

"I ask the people of Arizona and the people of America to keep the victims and their families in your prayers and to pray for their recovery and pray that we never again in Arizona experience a tragedy like this again," Brewer said.

Update at 4:45 p.m. ET

President Obama just addressed the nation from the White House.

He said Rep. Giffords "is battling for her life" and that five people have lost their lives, including U.S. District Judge John Roll. "We do not know yet what provoked this unspeakable attack," said Obama, who has pledged federal resources and has sent FBI Director Robert Mueller to the scene.

Giffords is "a friend of mine," Obama said. "She is not only an extraordinary public servant...she is warm and well-liked."

Obama said the shooting "is a tragedy for Arizona and for our entire country. What Americans do in times of tragedy is come together and support each other."

"Those who have been injured...we are rooting for them and I know Gabby is as tough as they come," Obama said. "We are going to get to the bottom of this and we are going to get through this."

Update at 4:14 p.m. ET

U.S. District Judge John Roll died in the Arizona attack in which Rep. Gabrielle Giffords, D-Ariz., and others were shot, according to the Associated Press.

The information was confirmed to the AP by David Gonzales, U.S. Marshal for Arizona.

Giffords, 40, is in her third term in Congress.

Update at 4:10 p.m. ET

The gunman being held in the shooting of Rep. Gabrielle Giffords, D-Ariz., and several others has been identified as Jared Loughner, according to people familiar with the investigation.

U.S. officials who provided Loughner's name to the AP spoke on condition of anonymity because they were not authorized to release it publicly.

Update at 4 p.m. ET

Dr. Peter Rhee, chief of trauma at the University of Arizona Medical Center, says Rep. Gabrielle Giffords, D-Ariz., is alive and out of surgery. Rhee said he is "very optimistic" about Giffords' recovery, but will monitor her closely in the next 24 hours before determining her prognosis.

Giffords, he said, was shot once in the head "through and through." Rhee said Giffords was "following commands" before the surgery. "I'm as optimistic as you can get in this situation," he said.

Rhee said the hospital received 10 patients from the scene. One child, a 9-year-old, has died, he said. Five patients are in critical condition and five are still being operated on, he said.

Update at 3:49 p.m. ET

The Pima County Sheriff's office in Arizona is holding a news conference right now. Deputy Rich Kastigar says a pistol with an extended magazine was involved in the shooting. There were 18 people injured.

Kastigar says law enforcement officers are pulling videotape from stores in the area where the shooting occurred to obtain evidence.

The first 911 call came in 10:11 a.m. Arizona time, he said. He would not comment about reports that a federal judge was shot, and only said another federal employee was "very seriously injured."

"This is a dynamic event and it is still involving," he said.

Kastigar said it was unclear how the shooter got into the shopping center event. No car has been recovered Saturday and investigators are questioning bus drivers.

Update at 3:40 p.m. ET

Rep. Gabrielle Giffords, D-Ariz., has been shot in the head and is in critical condition following a shooting earlier today at an event outside of a Tucson grocery store in her district.

C.J. Karamargin, a spokesman for Giffords, told the Associated Press that the congresswoman was in surgery as of 1 p.m. Arizona time. Karamargin said an unspecified number of Giffords' staff members were injured in the shooting. Karamargin said he had no other information on the conditions of the injured or on the circumstances of the shooting.

President Obama issued a statement, calling the shooting "an unspeakable tragedy."

"While we are continuing to receive information, we know that some have passed away, and that Representative Giffords is gravely wounded," Obama said.

"We do not yet have all the answers. What we do know is that such a senseless and terrible act of violence has no place in a free society. I ask all Americans to join me and Michelle in keeping Representative Giffords, the victims of this tragedy, and their families in our prayers."

Pima County (Ariz.) Sheriff Clarence Dupnik told MSNBC that Giffords, 40, is in critical condition and is still alive. Dupnik says five people were shot and killed in this incident and seven others were shot and wounded.

House Speaker John Boehner said in a statement that "this is a sad day for our country."

"An attack on one who serves is an attack on all who serve," Boehner, R-Ohio, said. "Acts and threats of violence against public officials have no place in our society."

House Minority Leader Nancy Pelosi, D-Calif., called Giffords "a brilliant and courageous member of Congress." Giffords was first elected in 2006, part of the freshman class that had ushered in a Democratic majority that made Pelosi the House speaker.

Rep. Trent Franks, R-Ariz., who serves with Giffords on the House Armed Services Committee, says Giffords is "a precious, decent human being and this tragedy is beyond my ability to articulate. ...She was just out there doing her job. I pray for her family, I pray for her."

An angry Franks told MSNBC "someone has stepped out of bounds of humanity."

Franks said on MSNBC there is "no way you can put a rational analysis on someone shooting a member of Congress doing her job. ...Whoever did this is either deranged or evil beyond words."

Earlier, there were conflicting reports from the scene in northwest Tucson. National Public Radio had reported that Giffords had died.

According to Arizona Public Media, a gunman ran up and started shooting while Giffords was hosting a "Congress in Your Corner" event.

In Arizona, Giffords represents the 8th District, which spreads to the U.S.-Mexico border. She won her third term in November by slightly more than 1 percentage point over Republican Jesse Kelly, who had Tea Party support.

Giffords, a centrist Democrat, is married to former Discovery astronaut Mark Kelly, who is of no relation to her former opponent. Giffords had made immigration and border control among her signature issues while in Congress.

Last March, shortly after the House passed health care, Giffords' congressional office in Tucson was vandalized. Someone had either kicked or shot out a glass door and window.

(Posted by Catalina Camia with reporting from Megan H. Chan and Kevin Johnson)