* Government says may be a "terrorist" attack
* Police, military moving through complex
* Somali militatants have threatened before to attack mall
By Edmund Blair and Goran Tomasevic
NAIROBI, Sept 21 (Reuters) - Gunmen stormed a shopping mall in Nairobi on Saturday killing at least 20 people in what Kenya's government said could be a terrorist attack, and sending scores fleeing into shops, a cinema and onto the streets in search of safety.
Sporadic gun shots could be heard hours after the assault started as soldiers surrounded the mall and police and soldiers combed the building, hunting down the attackers shop by shop. Some local television stations reported hostages had been taken, but there was no official confirmation.
The Somali militant group al Shabaab, which Kenya blames for shootings, bombings and grenade attacks against churches and the security forces, had threatened before to strike the Westgate mall, popular with the city's expatriate community. The chain of attacks follows action by Kenyan forces against al Qaeda-linked militants in Somalia two years ago.
Police helicopters circled above the mall as armed police shouted "get out! get out!" and scores of shoppers fled the building. Smoke poured out of one entrance of the high and witnesses said they heard grenade blasts.
Others said they saw about five armed assailants storm the beige stone Westgate shopping mall and that the incident appeared to be an attack rather than an armed robbery.
"They don't seem like thugs, this is not a robbery incident," said Yukeh Mannasseh who was on the mall's top floor when the shooting started. "It seems like an attack. The guards who saw them said they were shooting indiscriminately."
Kenya's Ministry of Interior said: "It is a possibility that it is an attack by terrorists, so we are treating the matter very seriously.".
Asked if foreign security services were involved in the operation to flush out the attackers, he said, "At this stage it has not become necessary yet."
One eyewitness who identified himself as Taha said he heard the screech of brakes followed moments later by an explosion and then sustained gun fire from the ground floor.
Another survivor said he was shot by a man who looked Somali.
Some shoppers ran up stairs and escalators and hid around the mall's cinema complex. Police found another terrified group hiding in a toilet on the first floor.
At least two dozen wounded were wheeled out on stretchers and shopping trolleys. Many of the victims had multiple light wounds, apparently from flying debris. Other walked out, some with bloodied clothing wrapped around wounds.
Reuters correspondents saw at least 20 bodies in two diferent locations.
The Kenyan Red Cross said at least 15 had been killed and more casualties were still inside the complex.
"The casualties are many, and that's only what we have on the outside," Kenya Red Cross Society Secretary General Abbas Guled said. "Inside there are even more casualties and shooting is still going on."
Al Shabaab have previously threatened to launch strikes on Nairobi's tower blocks and soft targets including nightclubs and hotels known to be popular with Westerners in the capital. But they have so far failed to carry out such an attack.
"I personally touched the eyes of four people and they were dead. One of them was a child," said one former British soldier at the scene.
"It's carnage up there."
Asked if the attack was a robbery, one paramilitary officer said: "No, terrorist". There has, though, been no official statement from the police regarding the attackers' motive.
Police cordoned off the roads surrounding the mall in central Nairobi's Westlands neighbourhood.
Satpal Singh, who was in another cafe on the mall's top floor said he ran downstairs when he heard the gunfire and was shot at near the mall's main exit.
"A Somali guy shot at me. The guy who shot me was carrying a rifle, an AK-47," 36-year-old Singh said.