BBC News -- President Mwai Kibaki has vowed to hunt down those who carried out a massacre in a north-east Kenyan village.
Hundreds of armed men surrounded a primary school and nearby houses and opened fire as children were making their way to school early on Tuesday.
Security forces say 56 people - including 22 children - died in the revenge attack by raiders feuding over water and pastures.
One mother watched as gunmen killed her two children and beheaded her husband.
"I appeal for calm as the government embarks on a security operation to track down the perpetrators of the attack," Mr Kibaki said.
Most of those killed were women and children, many of whom were under 10 years old, police said earlier.
Tuesday's raid in Turbi village - populated by the Gabra clan - is blamed on the rival Borana from Ethiopia. The two groups have feuded over water and pasture in the semi-arid region.
Cross-border raids for livestock are common in the area but correspondents say this is one of the most deadly such attacks in Kenya's history.
Ten Borana were killed in a revenge attack.
Superintendent Jasper Ombati told the BBC's Focus on Africa that the raiders were being pursued near the Kenya-Ethiopia border but refused to confirm that they came from Ethiopia saying this was being investigated.
"We have got a substantial number of security forces in the area," he said, "but the area is quite rugged and you have to go on foot."
Bodies have been left on the streets where they were killed.
Former Kenyan Foreign Minister Bonaya Godana, who toured the scene of the attack, told the AFP news agency that many of the victims were shot dead while getting ready to go to school.
He said most of the 22 children "died in their school uniforms".
In the nearest large town , Marsabit, 16 people are being treated in hospital, the BBC's Adam Mynott in northern Kenya says.
He says a truckload of villagers fleeing from the threat of further violence arrived in the town.
Grandmother Darare Bathacha told Kenya's Daily Nation newspaper that she had survived by crawling under a bed as the killers murdered her son, Ukur Boru, 40, his wife, Kabane Ukur and their nursery school age son.
Another survivor Okille Hukha, 46, ran into the bush but his wife and four children were all killed.
Galgalo Hukka, 28, told the newspaper that he fled from Turbi when the raiders struck at about 0600 local time "killing indiscriminately and looting household property and livestock".
"They caused havoc until 12pm and even when we left the town at 1pm, they had only retreated to some 800 metres away from the town.
"They were armed with rifles, hand grenades, machetes and spears," he said.
James Galgalo of the Catholic Justice and Peace Commission in Marsabit said he believed the raiders were seeking revenge for earlier attacks.
"There have been clashes all around here in the past three months between the Gabra and Borana," he told the BBC.
"They are massacring people - from what we saw they used a lot of spears and knives."
Kenya's media say dozens have been killed in clashes between the two ethnic groups this year.