Kenyan officials say the government has launched an investigation into a four-day siege at a partly Israeli-owned shopping mall in Nairobi that killed at least 72 people and destroyed part of the complex.

The officials said on Wednesday that US, British and Israeli agencies are helping the eastern African country in the probe.

A day earlier, Kenyan President Uhuru Kenyatta said that security forces had defeated Somalia’s al-Shabab fighters at the shopping center popular with rich Kenyans and foreigners.

According to reports, the dead also included three British nationals, two French women, two Canadian citizens, including a diplomat, a Chinese woman, two Indians, a Ghanaian poet, a South Korean, a South African, and a Dutch woman.

Al-Shabab officials have claimed responsibility for the assault and warned the Kenyan government to withdraw its troops from their country.

Late on Wednesday night, al Shabab leader Ahmed Godane confirmed that the group was behind the attack on the mall, saying the raid was in retaliation for the Kenyan military’s invasion of southern Somalia in October 2011.

"Take your troops out or prepare for a long-lasting war, blood, destruction and evacuation," Godane said in an audio message posted on an al Shabab-linked website.

"You are part of the massacre Kenya carried out in Kismayo and in other towns because you had elected your politicians. The tax you pay is used to arm Uhuru (Kenyatta) forces that massacre Muslims. You had supported the fight against us," Godane said in the message directed to Kenyans.

Kenya has more than 4,000 army soldiers in southern Somalia, where they have been battling the al-Shabab fighters since 2011.

The Kenyan troops are part of the African Union Mission in Somalia (AMISOM) that gets training and equipment from the United States.

Somalia has not had an effective central government since 1991, when warlords overthrew former dictator Mohamed Siad Barre.

However, MPs meeting in Mogadishu elected Hassan Sheikh Mohamud as the new president of Somalia with a big majority in September 2012.

The weak Western-backed government in Mogadishu has been battling al-Shabab fighters for more than six years and is propped up by the 10,000-strong AMISOM force from Uganda, Burundi, Djibouti, and Kenya.