Kenyan police have released a British man without charge after he was arrested in Nairobi following the attack on a shopping mall by Islamist militants, British sources said on Monday.

"We can confirm that a British national has been released from custody in Nairobi," a spokeswoman for the Foreign Office said.

Kenya has vowed not to bow to Shebab threats of more attacks if troops are not pulled out of Somalia, following a devastating mall attack in Nairobi by the Al-Qaida-linked insurgents.

"We went to Somalia because Al-Shebab was a threat to national security... We will continue to take action on that front until our security and interests in the country are protected," Interior Minister Joseph Ole Lenku told reporters on Friday.

Kenya's interior minister said Friday the country would not bow to Shebab demands to pull troops out of Somalia following a devastating mall attack in Nairobi by the al-Qaida-linked insurgents.

"We went to Somalia because Al-Shebab was a threat to national security... We will continue to take action on that front until our security and interests in the country are protected," Joseph Ole Lenku told reporters.

Somalia's Shebab on Friday threatened fresh attacks against Kenya, as police scoured the smoking rubble in Nairobi's Westgate mall devastated by their assault for bodies and clues.

The Al-Qaida linked Shebab gloated at the massacre of at least 67 people in the mall, which saw a group of gunmen storm the part Israeli-owned complex at midday Saturday, firing from the hip and hurling grenades at shoppers and staff, before holding off Kenyan and foreign forces with a barrage of bullets for four days.

Burundi and Uganda said Thursday they had beefed up security after the Shebab's deadly Nairobi mall attack amid fears the extremists would now strike Kenya's military partners in Somalia.

Kenya, Uganda and Burundi contribute most of the 17,700 soldiers in the African Union's AMISOM force battling the Shebab in Somalia.

The Shebab's bloody siege of a mall in Kenya confirms the Somali group's successful transformation from a guerrilla army into a leaner organisation focused on terrorist attacks, analysts said.

The September 21 raid and ensuing hostage crisis that killed at least 67 people was the most spectacular in the group's seven years of existence and boosted the Shebab's prestige in the jihadi world.

The Nairobi mall carnage in which several foreigners were killed by Islamist fighters was a "message to Westerners" who supported Kenya, Somalia's Shebab chief said in an audio message Wednesday.

Reclusive rebel supremo Ahmed Abdi Godane said the four-day bloodbath was a warning to Westerners who "backed Kenya's invasion (of Somalia) that has spilled the blood of the Muslims for the interest of their oil companies."

The Somalia-based militants who stormed a Kenyan mall had a detailed plan and had hidden weapons at the scene beforehand, according to U.S. officials cited by the New York Times Wednesday.

According to the report, a hand-picked group of English-speaking fighters from the Shebab, an Islamist rebel group, had trained for the assault in Somalia for weeks beforehand.

Impoverished Somali refugee camps in northern Kenya could not be more different from upmarket malls in the capital Nairobi, but attacks by Somalia's Shebab insurgents have affected them both.

Now, as Kenya reels from a four-day siege by the al-Qaida-linked gunmen in Westgate mall, Somalis in the country are terrified of retaliatory attacks.

Dozens of Americans have been lured away from comfortable homes to join Somalia's Shebab insurgents, the Islamist group behind the bloody attack on a Kenyan mall.

While the FBI said Tuesday it has not yet been able to confirm reports that two or three Americans were among the gunmen at Nairobi's Westgate mall, the news has the nation's Somali community on edge.