NAIROBI (AFP) - Kenyan troops backed by Israeli forces battled Sunday to end a siege in an upmarket shopping mall and free hostages held by Somali militants in an attack that has so far killed 59 people.

Sporadic gunfire could be heard as Kenyan security officials said they were attempting to kill or capture the remaining attackers and end the 26-hour-long bloodbath at the Westgate mall.

"The Israelis have just entered and they are rescuing the hostages and the injured," a Kenyan security source told AFP.

The Israeli foreign ministry refused to confirm or deny its forces were involved. "We don't make a habit of commenting on security cooperation of any kind that there may or may not be," spokesman Paul Hirschson told AFP.

Somalia's Al Qaeda-inspired Shebab rebels said the carnage at the part Israeli-owned complex was in retaliation for Kenya's military intervention in Somalia, where African Union troops are battling the Islamists.

Interior Minister Joseph Ole Lenku said 59 people were confirmed dead, while the Red Cross has estimated the number of injured at around 200.

Mr Lenku said there were still between 10 to 15 gunmen in the shopping centre.

"We believe there are some innocent people in the building, that is why the operation is delicate." Kenyan President Uhuru Kenyatta had said in a televised address to the nation late Saturday that he had lost family members in the attack.

"Let me make it clear. We shall hunt down the perpetrators wherever they run to. We shall get them. We shall punish them for this heinous crime," he vowed.

The Westgate mall is popular with wealthy Kenyans and expatriates, and was packed with around 1,000 shoppers when the gunmen marched in at midday on Saturday, tossed grenades and sprayed automatic gunfire at terrified people.

Security agencies have long feared that the shopping centre could be targeted by Al Qaeda-linked groups.

The attack was the worst in Nairobi since an Al-Qaeda bombing at the US embassy killed more than 200 people in 1998.