The Kenyan military says it has rescued "most" of the hostages who were held captive by Somalia’s al-Shabab fighters inside a partly Israeli-owned shopping mall in Nairobi.

Kenya Defense Forces (KDF) spokesman Cyrus Oguna made the announcement late on Sunday, adding that “security forces have taken control of most parts of the building.”

Kenyan and Israeli forces launched a major assault on Sunday evening to end the two-day standoff that killed at least 68 people and injured about 200.

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.

Kenyan police warned that the death toll could rise "much higher".

"This will end tonight. Our forces will prevail. Kenyans are standing firm against aggression, and we will win," Kenya's Disaster Operations Center said in a message on its Twitter page.

According to police, 10 to 15 heavily armed al-Shabab militants stormed the mall from two sides on Saturday.

Some militants have been killed and the security forces are battling the remaining attackers, police officials said.

"The criminals are now all located in one place within the building... We have as good a chance to successfully neutralize the terrorists as we can hope for," Kenyan President Uhuru Kenyatta said in a televised speech on Sunday afternoon.

A Kenyan security official confirmed that Israeli troops were involved in the operation. The official spoke on condition of anonymity because he was not authorized to talk to the media.

On Saturday, 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.

In another statement posted on Twitter on Sunday, the al-Shabab said that Kenyan officials were asking the hostage-takers to negotiate and offering incentives.

“We'll not negotiate with the Kenyan govt. as long as its forces are invading our country, so reap the bitter fruits of your harvest,” the tweet 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.