"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.
Somalia's Shebab chief Ahmed Abdi Godane said the Nairobi Westgate mall carnage in which at least 67 people were killed would be followed by "more bloodshed" unless Kenya left Somalia.
Kenya invaded southern Somalia to attack Shebab bases two years ago, and later joined the 17,700-strong African Union force deployed in the country.
Funerals continued Friday for the victims on the third and final day of official mourning, with President Uhuru Kenyatta attending the service of his slain nephew.
As well as scores of Kenyans, many of the dead were foreigners, including from Britain, Canada, China, France, the Netherlands, India, South Africa and South Korea.
Nigerian Nobel literature laureate Wole Soyinka and other writers paid tribute to renowned Ghanaian poet and statesman Kofi Awoonor who was among the dead.
"We denounce these enemies of humanity," Soyinka said, accompanied by several writers and authors at a press conference in Freedom Park in central Lagos, Nigeria's largest city.
Dozens more are unaccounted for, with 59 people still listed by the Red Cross as missing after the attack, one of the worst in Kenya's history.
The extremists Friday gloated at the massacre, 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.
"The mesmeric performance by the Westgate Warriors was undoubtedly gripping, but despair not folks, that was just the premiere of Act 1," the group said in one of a string of messages posted on social media.
Since the unprecedented 80-hour siege ended late Tuesday, the Shebab have claimed responsibility for an attack Thursday on a police compound on the border with Somalia, killing two officers.
Attacks are common in Kenya's northeastern border with Somalia, with regular grenade blasts or shooting ever since Kenyan troops crossed into southern Somalia two years ago.
Close to 200 people were wounded in the four-day mall carnage in one of Nairobi's largest shopping centres, which was popular among wealthy Kenyans, diplomats, UN workers and other expatriates.
Police continued to scour the fire-blackened rubble in Westgate for bodies and clues, with Lenku insisting that contents of smashed shops would be protected from looters.
Kenya's parliamentary defence committee meanwhile ordered army, security and intelligence chiefs to answer questions about the handling of the siege next week.
Police have pleaded for patience as Kenyan and international teams -- including from Britain, the United States, Israel, Germany, Canada and Interpol -- painstakingly examine the mall.
With around a third of the building collapsed -- as though hit by an earthquake -- and with the risk of booby traps amongst the mangled wreckage, the work of international forensic and security experts will take days to complete.
Several members of the Kenyan forces involved in battle inside the mall said that the fire broke out Monday after Kenyans fired at least two bazooka anti-tank rockets at the gunmen, who were holed up in the strong room of a supermarket.
"In the end we had to use full force, we had to finish with these guys," said one member of the elite force.
Top Interpol official Jean-Michel Louting, speaking near the mall, told AFP the challenge for investigators was to try "to remove the three levels that collapsed and see what is underneath".
Interpol issued an international arrest notice at Kenya's request for 29-year-old Samantha Lewthwaite, dubbed the 'White Widow', a reference to her marriage to one of the suicide bombers who killed 52 people in London's July 2005 terror attacks.
Nairobi accuses her of alleged links to the Shebab and the possession of explosives in a 2011 plot, and there has been widespread media speculation over her possible role in Nairobi's deadly siege, despite no concrete evidence so far.
Five suspected attackers were killed in the mall and eight other people detained, officials said. Three others have since been released without charge.
Kenya further sought to shrug off the threats with the government issuing a defiant statement to say plans to raise close to $1.5 billion (1.1 billion euros) in a debut international bond issue were unaffected.
"The Kenyan economy, just like the spirit of our people, is unshaken by the recent tragedy," Treasury Secretary Henry Rotich said in a statement.
Still the country remains traumatised.
Somalis living in Kenya are terrified of retaliatory attacks, against the half a million refugees as well as members of the native ethnic Somali community.
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