Update 2:30 p.m. EDT: Kenyan officials tell the Associated Press an operation to end the siege has begun and it will be over "tonight."
Reuters reported the sounds of gunfire and an explosion. Two helicopters were seen over the area, and mobile phone signals were cut.
Update 2 p.m. EDT: The Keynan Red Cross says nine more bodies have been recovered, raising the confirmed death toll to 69.
Update 10 a.m. EDT: President Uhuru Kenyatta said 10 to 15 armed terrorists and their hostages remain cornered in a section of the Westgate Shopping Centre, the BBC reports.
CNN reported the hostages number around 30.
Kenyatta said his nephew and the nephew's fiancee were among those killed in the attack.
The siege at a Nairobi Kenya shopping mall continued Sunday as Somali Islamist militants were holed up with dozens of hostages. At least 59 people have been killed, Kenyan authorities said.
A volley of gunfire Sunday lasting about 30 seconds interrupted a stalemate of several hours, a witness told Reuters, speaking from close to the Westgate shopping center, which has several Israeli-owned outlets and which is frequented by expatriates and Kenyans.
Agence France-Presse reported that Israeli commandos were assisting the Kenyan troops trying end the standoff.
"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.
Among the foreigners killed in Saturday’s attack were two diplomats - one from Canada and another from Ghana – Reuters reported. U.S. Secretary of State John Kerry, who offered assistance to Kenya, said several U.S. citizens had been wounded and the wife of a U.S. diplomat working for the U.S. Agency for International Development was killed.
Somalia's al-Qaeda-inspired al-Shabaab rebels claimed the raid, saying it was in retaliation for Kenya's military intervention in Somalia, where African Union troops are battling the Islamists.
"We have warned Kenya of that attack but it ignored (us), still forcefully holding our lands... while killing our innocent civilians," Shabaab spokesman Sheik Ali Mohamud Rage said in a statement. "If you want Kenya in peace, it will not happen as long as your boys are in our lands."
The group also issued a string of statements via Twitter, one of them claiming that Muslims in the mall had been "escorted out by the Mujahideen before beginning the attack."
Kenya Interior Minister Joseph Ole Lenku said 59 people were confirmed dead, while the Red Cross has estimated the number of injured at around 200.
Lenku said there were still between 10 to 15 gunmen in the shopping center. "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. For hours after the brazen attack on Saturday, the dead were strewn around tables of unfinished meals. At one burger restaurant, a man and woman lay in a final embrace after they had been killed, before their bodies were removed. Pop music was left playing.