The cause of the blast was not clear, but police Commissioner Mohamed Hussein Ali said the explosive device was "something that somebody was carrying." In response to questions about whether it was a suicide attack, he said: "That type of speculation is not factual at all."
Police said in a written statement that no traces of "high explosives" were detected at the scene.
Linet Atieno, spokeswoman of the Kenya Red Cross, said two people were killed in the blast.
Health Minister Charity Ngilu told journalists 33 injured had been hospitalized, among them four taken immediately into surgery and six others badly hurt.
The initial investigation shows that a man got off a minivan taxi and a guard tried to stop him from entering a small restaurant because he was wearing something that looked suspicious, police officers at the scene said.
The explosion occurred shortly after, said the officers, who spoke on condition of anonymity because they were not authorized to speak to journalists.
They said it was not clear whether the man had anything to do with the bombing and they had no other details.
Police spokesman Eric Kiraithe said authorities were testing debris for traces of explosives and that they were working with local and foreign laboratories to examine the evidence.
"Police investigators are pursuing promising leads to ascertain the identity of the perpetrators and possible motive that led to this incident," he said.
Witnesses gave differing accounts, a reflection of the initial confusion.
Two men who said they witnessed the explosion told The Associated Press they saw a man who left a black bag near a shoe shiner run away and then there was a blast.
"The black bag was left on the ground when this man hit me," as he ran away, said Robert Maritim, who had just finished having his shoes shined. Maritim, 24, said he fell down and as he was getting up, the explosion lifted him off the ground and he landed on a tree. One of the men shining shoes was injured, he said.
"I don't know what his (the shoe shiner's) chances of survival are. The person who was brushing my shoes is OK and I am thanking God," said Maritim, who declined to give his profession.
Edward Tongai, 36, who was shining Maritim's shoes, said the other shoe shiner, "was shouting for his money as the tall man started running and hit Maritim."
A man who said he witnessed the explosion said that the blast struck two men in their 30s who were walking together.
"One of the men, who was carrying a rucksack was lifted off the ground and when he came down, he did not move ... The other man was injured on both legs but when we tried to assist, he refused our help," Joshua Kinyazui told The Associated Press. "The explosion caused papers to scatter all over and police then came and took the injured man away."
An Associated Press reporter saw a body lying outside a small restaurant where the windows were blown out, with shards of glass strewn on the pavement.
The shop was on the ground floor of one of Nairobi's oldest hotels, the Ambassadeur Hotel, which has a largely Kenyan clientele. Part of the hotel's parking area also serves as a terminus for buses and minivan taxis. The hotel itself was not affected by the blast.
Police were trying to clear the area as hundreds of people gathered around.
Ali urged the public to be "extremely careful" about speculating on the nature of the explosion.
The last major bombing in Nairobi was in 1998, when the U.S. embassies in downtown Nairobi and Dar es Salaam, Tanzania were simultaneously hit, killing 225 people. An East Africa al-Qaida network was blamed for that bombing.
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