British Prime Minister David Cameron says three Britons were killed in the attack and siege at an upscale Nairobi shopping mall.

"It is an absolutely sickening and despicable attack of appalling brutality. What we know is that three British nationals have been killed. Because the situation is ongoing we should prepare ourselves for further bad news," Cameron said.

The three Britons are among a number of foreign nationals who were killed as gunmen from the Somali militant group al Shabaab stormed the Westgate mall on Saturday in an assault and siege that was still ongoing on Sunday.

The confirmed death toll on Sunday reached 59 with more than 170 wounded.

"I think that the other thing to remember is that these appalling terrorist attacks that take place, where the perpetrators claim they do it in the name of a religion, they don't. They do it in the name of terror, violence, extremism and their warped view of the world. They don't represent Islam or Muslims in Britain or anywhere else in the world," Cameron said warning Britons to be braced for "more bad news".

Among other foreigners, Canada said at least two of its nationals were killed, including a diplomat, and both France and India confirmed that two apiece of their citizens had been killed. A diplomat from Ghana was also among the dead.

Throughout the day on Sunday al Shabaab militants have been at bay with hostages in the shopping center, which was sealed off by Kenyan security forces, as Kenya said some 10 to 15 attackers remained at large inside.

The Islamist group opposes Kenya's participation in a peacekeeping mission in neighboring Somalia.

Brief volleys of gunfire interrupted hours of stalemate in the late afternoon.

A Reuters correspondent saw security personnel on the move and as dusk closed in two helicopters swooped low over the mall which has several Israeli-owned outlets and is frequented by many foreigners.