Gabrielle Giffords, right, the Democrat representative for Arizonas 8th district,

in Washington last week. Photograph: Susan Walsh/AP

A US congresswoman was shot in the head at point blank range yesterday and six people were killed at a public meeting outside a grocery shop in Arizona. The dead included a nine-year-old girl and a federal judge.

Gabrielle Giffords, a 40-year-old Democratic member of the House of Representatives, was airlifted to University Medical Centre in Tucson after being targeted by a 22-year-old army reject. A surgeon at the hospital said Giffords was in a critical condition following emergency surgery last night, but added: "I am very optimistic about her."

Describing the shooting as "an unspeakable tragedy", President Barack Obama asked people to pray for "a friend of mine" who was battling for her life. "While we are continuing to receive information, we know that some have passed away, and that Representative Giffords is gravely wounded," he said. "Gaby is not only an extraordinary public servant but also someone who is warm and kind, who was liked by her colleagues and her constituents."

As Obama ordered the FBI director, Robert Mueller, to Tucson to oversee the investigation, Arizona sheriff Clarence Dupnik said police had a photo of a second man they are hunting who they thought was also involved in the attack.

Giffords's assailant was last night named as Jared Lee Loughner. He was described by a doctor who treated some of the victims at the scene as a young white man with a "determined look on his face" and wearing dark clothing.

After shooting Giffords, he used an automatic weapon to shoot at up to 30 people leaving several dead and 13 wounded, many of whom were also airlifted to hospital. Among the dead, according to Pima County sheriffs, were the child, and the US District Judge John Roll, who had been involved in immigration cases and had previously received death threats.

Only when Loughner ran out of ammunition did he attempt to flee. One of Giffords's aides tackled the assailant and helped to pin him down until police arrived.

Giffords had been named as a political campaign target for conservatives in last November's mid-term elections by former Alaskan governor Sarah Palin because of her strong support for Obama's health reforms. Palin had published a "target map" on her website using images of gun sights to identify 20 House Democrats, including Giffords, for backing the new healthcare law.

While the motive for the shooting was not immediately clear, Giffords is one of 10 Democrat members of Congress who were the subject of ha****ment over their support for the healthcare overhaul. Giffords's Tucson constituency office was vandalised last March after she voted in favour of Obama's controversial health bill, which has been bitterly opposed by the American right.

In an interview after the vandalism, Giffords referred to the animosity against her. "We're on Sarah Palin's targeted list," she said, "but the thing is, the way that she has it depicted has the crosshairs of a gun sight over our district. When people do that, they have to realise that there are consequences to that action."

Palin came under huge criticism for her campaign and issued a statement via her Facebook page last night offering her "sincere condolences" to Giffords and her family.

The shooting happened shortly after 10am local time outside a Safeway store in Tucson. Loughner ran up and opened fire on Giffords while she was talking to a couple. The event, called "Congress on Your Corner", was designed to allow members of Giffords's 8th Congressional district to meet her face to face. The congresswoman herself had used Twitter shortly before the shooting, saying: "My first Congress on Your Corner starts now. Please stop by to let me know what is on your mind or tweet me later."

Witnesses said that the gunman ran into a "crowded area" and began "firing indiscriminately". Andrea Gooden, who was working across the road from the scene, said: "I heard about 15 shots. Then there were people racing across the parking lot."

Another witness, Steven Rayle, who helped restrain Loughner, said: "The event was very informal. Giffords had set up a table outside the Safeway and about 20 or 30 people were gathered to talk to her. The gunman, who may have come from inside the Safeway, walked up and shot Giffords in the head first."

Jason Pekau, an employee at a shop close to the shooting, said two bodies were covered on the pavement after emergency services had arrived at the scene.

Giffords, who was born in Tucson and has two children, took office in January 2007 supporting immigration control, embryonic stem-cell research and the right to abortion.

Representative Jerrold Nadler, a New York Democrat, told CNN that Giffords's office had been shot at before and that she had received death threats in the past. At another event in 2009 which was similar to the one Giffords was holding, a protester was removed by police when his pistol fell to the supermarket floor.

Although a Democrat, Giffords was a strong supporter of the right to bear arms and was re-elected to her third term last November, edging out the Tea Party favourite Jesse Kelly.

Giffords is married to space shuttle astronaut Mark Kelly, and is the first Jewish woman elected to Congress from Arizona and the third female ever to be elected for that state. She has been building up a prominent public profile, with frequent appearances in the national media.

The US Capitol Police force said that it was advising Congress representatives and their aides to "take reasonable and prudent precautions" about their own security in the wake of the shooting.