Canadian Prime Minister Stephen Harper says two nationals of his country, including a diplomat, are among the dozens of people killed in Saturday’s attack in a partly Israeli-owned shopping mall in the Kenyan capital Nairobi.

Kenyan President Uhuru Kenyatta said on Saturday that at least 39 people had been killed, including close members of his own family, and more than 150 others injured in the attack on Nairobi's Westgate shopping mall

"Canada condemns in the strongest possible terms this cowardly, hateful act that apparently targeted innocent civilians who were simply out shopping," Harper said in a statement issued on Saturday night.

The Canadian prime minister said diplomat Annemarie Desloges, who was a liaison officer with the Canada Border Services Agency at Canada's High Commission to Kenya, would be "remembered and honored."

"Terrorist attacks like this seek to undermine the very values and way of life that Canadians cherish, and they reinforce the need for us to continue taking strong actions to protect the safety of Canadians no matter where they are in the world," he added.

Earlier in the day, the United States said several Americans were also injured in the attack in Nairobi.

Somalia’s al-Shabab fighters claimed responsibility for the assault and warned the Kenyan government to withdraw its troops from their country.

"The Christian government of Kenya invaded our country in October 2011 killing many innocent civilians with their military jets," al-Shabab spokesman Sheik Ali Mohamud Rage said.

"We have warned Kenya of that attack, but it ignored (us), still forcefully holding our lands ... while killing our innocent civilians," Rage said.

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.