David Cameron has expressed his shock and sadness at the assassination attempt on a US politician which killed six people, including a young girl.
Congresswoman Gabrielle Giffords, who was shot through the head by a gunman at a public event, remains in a critical condition in hospital.
A 22-year-old suspect, named as Jared Loughner, is being held in custody and US police are also searching for a possible accomplice.
In a message sent to US President Barack Obama, the Prime Minister extended Britain’s sympathies and said “violence and hate” must not be allowed to stifle political debate.
“Like everyone in Britain, I was shocked and saddened by the shootings which took place in Tucson, Arizona,” he told the president.
“Our hearts go out to all of those who have been caught up in this terrible incident.
“That such an attack should have taken place against a member of Congress as she was meeting her constituents in a shopping centre on a Saturday morning is especially shocking to all of us who believe in democracy.
“I am keeping Representative Giffords in my thoughts and prayers as she battles for life, together with all of those who have been wounded. And please would you pass on my deep sympathies to the families of those who sadly lost their lives.
“As you said, at times of tragedy like this Americans come together. We stand with you at this difficult time, and in our shared belief that we must never allow violence and hate to extinguish the open political discourse which is our surest protection.”
Shadow foreign secretary Yvette Cooper said: “The tragedy in Arizona is truly appalling. Congresswoman Giffords and those at this public event were involved in something so normal yet important for any democracy: meeting, talking and debating. Our thoughts are with those who have lost loved ones and wishes for a speedy and full recovery are with those who have been injured.”