The AFP journalist viewed two bodies, while the Red Cross said on its Twitter account that seven people had also been wounded in an attack on a restaurant in the Dadaab refugee camp complex, the world’s biggest, which lies about 100km from the border with Somalia.
“We lost two people and others have been injured,” regional police chief Philip Tuimur said.
A police source who requested anonymity said the grenade was thrown from a moving vehicle.
Dadaab has sheltered Somalis fleeing violence and drought for more than 20 years, and their numbers currently stand at nearly half a million.
Attacks have increased within Kenya since Nairobi sent army soldiers into southern Sudan to fight Somalia’s al-Qaeda linked al-Shabaab insurgents in late 2011.
Similar attacks and cross-border raids in the region have been blamed on the insurgents or their Kenyan supporters, who have vowed revenge.
The Shabaab still control large parts of southern Somalia, despite African Union troops, allied Somali forces and Ethiopian soldiers having wrested control of several key towns.
Kenyan troops, now integrated into the African Union force, seized the Shabaab bastion of Kismayo, a key southern Somali port, in September. That led to warnings of retaliation from both the Islamist insurgents and their Kenyan supporters.
But the Shabaab have denied involvement in previous similar bombings.
Violence in Kenya – ranging from attacks blamed on Islamists, inter-communal clashes and a police crackdown on a coastal separatist movement – have raised concerns over security ahead of elections due in March 2013.
Five years ago, elections descended into deadly post-poll killings that shattered Kenya’s image as a beacon of regional stability.
In Somalia in 2011, famine caused by extreme drought exacerbated by conflict claimed tens of thousands of lives and affected more than four million people, according to the United Nations.
Over a million Somalis are displaced inside the country, while over a million are refugees in neighbouring nations, according to UN figures.
Somalia has been in political chaos and deprived of an effective central government since the fall of President Siad Barre in 1991.
However, a new administration took office last September, ending eight years of transitional rule by a corruption-riddled government.
In recent months, the 17 000-strong African Union force, fighting alongside government troops and Ethiopian soldiers, have wrested a string of key towns off the extremist Shabaab.
The United Nations in December appealed for $1.3bn to support 3.8 million people – about half the population of the war-torn country – it said are in need.- AFP