Women and children run for cover
Women and children run for coverReuters

Israel security forces have joined their Kenyan counterparts in the fight to rescue hostages captured by Islamist terrorists at a Nairobi mall.

"The Israelis have just entered and they are rescuing the hostages and the injured," a security source said on condition he not be named.

An Israeli foreign ministry spokesperson would neither confirm nor deny the reports.

"We don't make a habit of commenting on security cooperation of any kind that there may or may not be," Paul Hirschson told AFP.

Israel and Kenya have a long history of friendly ties and close security and intelligence cooperation.

The latest development comes as the death toll in a bloody shooting spree by Islamist terrorists at a shopping mall in the Kenyan capital of Nairobi continues to rise, as several gunman have barricaded themselves in the mall, along with a number of hostages.

Officials in the east African country have raised the official death toll to 59, many of them children and the elderly, after gunmen from the Al Qaeda-linked Somali terrorist group Al Shabaab embarked on a bloody rampage through the luxurious Westgate mall in Nairobi. A further 175 people are believed to have been injured in the attack.

According to numerous media and official reports, as of this morning between 10-15 gunmen remain inside the mall, along with approximately 30 hostages, and were holding out against Kenyan security forces.

Witnesses described how the terrorists opened fire with assault weapons, mowing down men, women, children and the elderly.

The attack was not entirely "indiscriminate," however: multiple eyewitnesses described how victims were "vetted" by the terrorists, who made them recite Muslim prayers to ascertain their religion. Those who were able to prove that they were Muslim were allowed to go free, while non-Muslims were deliberately murdered in cold blood.

On its official "Twitter" account, Al Shabaab confirmed that Muslims had been "escorted" to safety, whilst "infidels" were targeted for death, and claimed to be holding at least 36 hostages.

One man described to how the terrorists methodically selected their victims.

"They came and said: 'If you are Muslim, stand up. We've come to rescue you'," Elijah Lamau told the BBC.

He said that the Muslims left with their hands up, following which the terrorists gunned down two people.

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 Saturday, tossed grenades and sprayed automatic gunfire at terrified people. The mall was targeted on an especially busy day, as the weekend rush reached its height with Kenyans and foreign tourists visiting its shops, restaurants and cinemas.

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

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

After a day and night of sometimes ferocious gun battles, security sources said police and soldiers had finally "pinned down" the gunmen. The Kenyan Red Cross appealed for blood donations and authorities urged residents to steer clear of the area.    

"We are still battling with the attackers and our forces have managed to maroon the attackers on one of the floors," said Kenyan military spokesman Colonel Cyrus Oguna. "We hope to bring this to an end today."