"We stand with the people of Kenya during this trying moment. We have sent our condolences to the families and we hailed the government of Kenya in the manner in which they've handled the crisis," Deputy Chairman of the African Union (AU) Erastus Mwecha said.
He added that the AU is working with its international partners to assist Kenya, following the terrorist attack on the West Gate Shopping Mall in the Kenyan capital of Nairobi.
"We've indicated our resolve to continue to fight terrorism in whatever form it exists. We are also aware that this is a global menace and we need to act together as an international community to fight the scourge," Mwecha said.
South Africa's ruling Africa Nationalist Congress (ANC) condemned the attack at the shopping mall and extended their "heartfelt condolences to the families of victims, the injured and to the general population of Kenya during this tragic time".
The ANC also supported calls by Kenya's President Uhuru Kenyatta, former prime minister Raila Odinga as well as the international community that those responsible be found and punished.
A South African was killed during the shootout at the mall. The Star newspaper has identified the victim as James Thomas, a 57 years old businessman from Cape Town, who was in Kenya for business.
Ghana also suffered a loss as among the dead was Kofi Awoonor, former chairman of Ghana's council of state, who was in Nairobi to deliver a lecture.
Ghana's President John Dramani Mahama expressed deep shock at the death and said it was "a sad twist of fate".
The Kenyan president described the massacre as an "evil and cowardly act of terrorism" and vowed to continue to fight against the Somali militants.
"I want to be very clear and categorical: We shall not relent on the war on terror. We will continue that fight, and we urge all people of goodwill throughout the world to join us and to ensure that we uproot this evil," he said.
Some analysts have traced Kenya's problem with Al Shabab group to the recognition provided by it to the Somali Transitional Federal government.
In addition, the Kenyan government last year restored order in some provinces of Somalia, with which it shares a 400-mile border, together with other AU peace-keepers, and this had angered some members of Al Shabaab.