Somalia's exiled government has condemned the killing of a BBC producer in the capital, Mogadishu.
Ms Peyton had worked in Africa for 10 years
Prime Minister Ali Mohammed Ghedi called it a "savage act", while his deputy said: "We cannot allow the forces of darkness to succeed."
Kate Peyton was shot in the back after speaking to government officials who had gone to Somalia to see if it was safe for them to relocate from Kenya.
The UK foreign office and journalist groups have also expressed their shock.
Ms Peyton's body has been flown to the Kenyan capital, Nairobi.
Mr Ghedi said the killing was intended to portray "Mogadishu as unsafe, and discourage international support for peace and reconciliation of Somalia".
The country has not had a functioning national government for 14 years, and rival warlords have battled for control of the capital.
The new government was named earlier this year after more than two years of talks in Kenya.
Ms Peyton was shot just hours after Mr Ghedi said that the government would start to move to Mogadishu on 21 February.
She was hit by a bullet from a passing car outside the Sahafi Hotel, where she and her colleague Peter Greste had spoken to government officials and MPs.
Mr Greste was not injured.
The team had just arrived in Mogadishu.
Ms Peyton was taken to hospital, where she had an operation on a bullet wound to her back, but died later of internal bleeding, the BBC said.
Ms Peyton's bodyguards gave chase to the gunmen and recovered the car but the occupants had fled.
Mr Ghedi also promised to catch the killers and offered a reward for information leading to their capture.
"We will investigate the murder of Ms Peyton and bring the perpetrators of this crime to justice," he said in a statement sent to the BBC in Nairobi.
Head of BBC News Helen Boaden said she would be "greatly missed".
Ghedi promised to bring the killers to justice
"Kate was one of our most experienced and respected Foreign Affairs producers who had worked all over Africa and all over the world.
BBC director general Mark Thompson said he was "profoundly shocked and saddened" by Ms Peyton's death.
"Kate had worked for the BBC since 1993 and was dedicated to covering news across the African continent."
The Foreign Office has also paid tribute to Ms Peyton.
"She had travelled with the foreign secretary abroad and was well known to our media staff wherever she went," it said in a statement.
Ms Peyton, who grew up in Suffolk, had spent the past 10 years in Africa and was based in Johannesburg. She had worked for the BBC as a producer and reporter since 1993.
Her friend and colleague BBC correspondent Fergal Keane said Ms Peyton was "the kindest, gentlest human being to work with and to have as a friend and I will always treasure her laughter and stories".
"She devoted a large part of her life in trying to telling the truth about Africa," he added.
The National Union of Journalists, of which Ms Peyton was a member, has condemned the killing and called for a "full investigation" into the circumstances.