Media playback is unsupported on your device Media caption Thousands of people listened to President Barack Obama's speech at the University of Arizona

President Barack Obama has paid tribute at a memorial service in Arizona to the six people killed and 13 injured in Saturday's shooting in Tucson.

He said he could not "fill the hole" torn in US hearts, but urged the nation to honour the victims through unity.

He said lawmaker Gabrielle Giffords, who was hurt in the attack, had opened her eyes for the first time that night.

Suspected gunman Jared Loughner has been charged with several offences and could face the death penalty if guilty.

More than 14,000 people gathered for the service at the University of Arizona's basketball arena, the McKale Memorial Center, in Tucson.

"There is nothing I can say that will fill the sudden hole torn in your hearts," said Mr Obama.

"But at a time when our discourse has become so sharply polarised - at a time when we are far too eager to lay the blame for all that ails the world at the feet of those who think differently than we do - it's important for us to pause for a moment and make sure that we are talking with each other in a way that heals, not a way that wounds."

At the scene It was a night of prickling emotions in the McKale Memorial Center. Many of the 14,000 within - and those filling the overflow area - had queued for hours. As they waited inside the centre cheers went up, for the doctors from the University Medical Center, relatives of the injured, state and national representatives. A huge cheer - almost a howl of pleasure and longing - went up for Barack and Michelle Obama as they came in. The president of the University of Arizona, Robert Shelton, spoke of Tucson as a small college town - "in the truest and best sense of the word, a community" - and it felt like that inside the arena. It felt like a city aching to come together after a grievous blow. And the president? Grim-faced, he took the platform as the crowd stood and applauded. Repeatedly, he invoked the Scriptures. He paid homage to the fallen, to the injured and to the heroes of that sunny Saturday morning. "There is nothing I can say that will fill the sudden hole torn in your hearts," he said. He was right. But he came close. Obama's call to 'moral arms'

The president added that it was impossible to know "what might have stopped those shots from being fired or what thoughts lurked in the inner recesses of a violent man's mind".

Mr Obama then praised the bravery of those who stopped the gunman while he paused to reload.

"Heroism is here all around us, in the hearts of so many of our fellow citizens, just waiting to be summoned - as it was on Saturday morning," he said.

Speaking before the president, Arizona Governor Jan Brewer said: "We will go forward unbending and unbowed."

"We know that the violence that occurred Saturday does not represent this community, this state or this country," said Homeland Security Secretary and former Arizona Governor Janet Napolitano.

The first stop for the president after arriving in Tucson was the hospital where Ms Giffords and others are being treated.

Ms Giffords, a Democrat, remains critically ill after being shot through the head in the attack outside a grocery store where she was holding a constituency event.

Mr Obama spent 10 minutes with Ms Giffords and her husband, Mark Kelly, before meeting four others injured in the shooting, including two of Ms Giffords' staff members.

During his speech at the memorial service, the president said Ms Giffords had opened her eyes a few minutes after he left her room in the hospital, for the first time since she was hospitalised.

"Gabby opened her eyes. So I can tell you she knows we are here. She knows we love her. And she knows that we are rooting for her through what is undoubtedly going to be a difficult journey," he said.

Former House Speaker Nancy Pelosi, Senator Kirsten Gillibrand and Representative Debbie Wasserman Schultz - all friends of Ms Giffords - were in the room when she opened her eyes.

House resolution

Before the service, Mr Obama also held private meetings with the families of those hurt and killed.

Among the six who died were a nine-year-old girl, a prominent judge and one of Ms Gifford's aides, who was engaged to be married.

Suspect: Jared Loughner Aged 22; lives with parents in Tucson

Described by former class-mates as "disruptive" drug-user and a loner

Reportedly posted series of rambling messages on social networking websites

Online messages show deep distrust of government and religion, calling US laws "treasonous" and calling for creation of a new currency

Was rejected by the US Army for drug use Profile: Jared Loughner

Mr Obama said he hoped the US would "live up" to the expectations of Christina Taylor Green, who was born on 9/11 but died during the shooting.

"I want our democracy to be as good as she imagined it," Mr Obama said of Ms Green, who had shown an early interest in public service.

Mr Loughner, 22, has been jailed pending trial. The case has been assigned to California federal Judge Larry Burns.

All judges in Arizona recused themselves from Mr Loughner's trial because federal Judge John Roll of Arizona was among those killed.

The US House of Representatives on Wednesday took up a resolution honouring Ms Giffords and other victims of the attack, with House Speaker John Boehner fighting back tears as he spoke of his ailing colleague.

Police stop

Earlier, former Alaska Governor Sarah Palin attacked as a "blood libel" suggestions that political rhetoric may have contributed in some way to the fatal shootings in Arizona.

Some commentators have specifically criticised Ms Palin for using an online graphic containing crosshair symbols that marked targeted Democratic districts in the US mid-term elections.

New details also began to emerge on Wednesday about the hours before the shooting took place.

Police have said Mr Loughner was given a verbal warning for running a red light hours before he allegedly opened fire on the crowd outside the supermarket.

Investigators have also said they found a handwritten note among Mr Loughner's effects where he lived in Tucson bearing the words "Die, bitch", which they believe was a reference to Ms Giffords.