Israel's Foreign Ministry reported that three Israelis were rescued from the mall. Israel's ambassador to Kenya and the Israeli security officer are at the scene and in direct contact with Kenyan security forces.
It was further reported that it appears the event is local and has no connection to Israel.
The al-Qaeda-linked Somali al-Shabab group claimed responsibility for the attack.
A statement on its official Twitter feed Saturday says the attacks are retribution for military action by Kenya inside Somalia. The group said it was now shifting the battlefield to Kenya.
The group said its fighters entered Nairobi's upscale Westgate Mall at around noon and were still inside more than nine hours later. Kenyan military special forces had entered the mall in an effort to end the standoff.
One gunman involved in the attack died from gunshot wounds shortly after he was arrested by Kenyan security forces, the Kenyan Presidency said on Twitter.
The al-Qaeda-linked gunmen asked the victims they had cornered if they were Muslim: If the answer was yes, several witnesses said, those people were free to go. The non-Muslims were not.
The assault killed at least 30 people, the Red Cross said, with fears the toll could rise further. As night fell in East Africa's commercial capital, hostages remained inside the mall, but officials didn't or couldn't say how many. Two groups of army special forces troops had moved inside as the stand-off stretched into its ninth hour.
Police and military surrounded the huge complex as helicopters buzzed overhead. An Associated Press reporter said he saw a wounded Kenyan soldier put into an ambulance at nightfall, an indication, perhaps, of a final shoot-out inside.
Witnesses said at least five gunmen - including at least one woman - first attacked an outdoor cafe at Nairobi's Westgate Mall, a shiny, new shopping center that hosts Nike, Adidas and Bose stores. The mall's ownership is Israeli, and security experts have long said the structure made an attractive terrorist target.
The attack began shortly after noon with bursts of gunfire and grenades. Shoppers -- expatriates and rich Kenyans - fled in any direction that might be safe: into back corners of stores, back service hallways and bank vaults. Over the next several hours, pockets of people poured out of the mall as undercover police moved in. Some of the wounded were being transported in shopping carts.
"We started by hearing gunshots downstairs and outside. Later we heard them come inside. We took cover. Then we saw two gunmen wearing black turbans. I saw them shoot," said Patrick Kuria, an employee at Artcaffe, the restaurant with shady outdoor seating.
Frank Mugungu, an off-duty army sergeant major, said he saw four male attackers and one female attacker. "One was Somali. The others were black," he said.
Al-Shabab, on its Twitter feed, said that it has many times warned Kenya's government that failure to remove its forces from Somalia "would have severe consequences." The group claimed that its gunmen had killed 100 people, but its claims are frequently exaggerated.
"The attack at #WestgateMall is just a very tiny fraction of what Muslims in Somalia experience at the hands of Kenyan invaders," al-Shabab said. Another tweet said: "For long we have waged war against the Kenyans in our land, now it's time to shift the battleground and take the war to their land #Westgate."
Al-Shabab threatened in late 2011 to unleash a large-scale attack in Nairobi. Kenya has seen a regular spate of grenade attacks since then but never such a large terrorist assault.
Kenya Red Cross official Abbas Gullet said at least 30 people were killed in Saturday's attack.
Nairobi's mortuary superintendent, Sammy Nyongesa Jacob, said Africans, Asians and Caucasians were among the bodies brought to the mortuary.
The State Department said it had reports of American citizens injured in the attack but had no further details. It condemned "this senseless act of violence that has resulted in death and injury for many innocent men, women, and children."
The US embassy said it was in contact with local authorities and offered assistance. Some British security personnel assisted in the response.
'Gunman told Muslims to leave'
The gunmen told hostages that non-Muslims would be targeted, said Elijah Kamau, who was at the mall at the time of the midday attack.
"The gunmen told Muslims to stand up and leave. They were safe, and non-Muslims would be targeted," he said.
Jay Patel, who sought cover on an upper floor in the mall when shooting began, said that when he looked out of a window onto the upper parking deck of the mall he saw the gunmen with a group of people. Patel said that as the attackers were talking, some of the people stood up and left and the others were shot.
The attack was carried out by terrorists, said police chief Benson Kibue. He did not specify a group. He said it was likely that no more than 10 attackers were involved.
Somalia's president -- the leader of a country familiar with terrorist attacks -- said his country knows "only too well the human costs of violence like this" as he extended prayers to those in Kenya.
"These heartless acts against defenseless civilians, including innocent children, are beyond the pale and cannot be tolerated. We stand shoulder to shoulder with Kenya in its time of grief for these lives lost and the many injured," President Hassan Sheikh Mohamud said.
The gunmen carried AK-47s and wore vests with hand grenades on them, said Manish Turohit, 18, who hid in a parking garage for two hours.
"They just came in and threw a grenade. We were running and they opened fire. They were shouting and firing," he said after marching out of the mall in a line of 15 people who all held their hands in the air.
A local hospital was overwhelmed with the number of wounded being brought in hours after the attack, so they had to divert them to a second facility. Dozens of people were wounded. Officials said Kenyans turned out in droves to donate blood.
The United Nations secretary-general's office said that Ban Ki-moon has spoken with President Uhuru Kenyatta and expressed his concern. British Prime Minister David Cameron also called Kenyatta and offered assistance.
Kenyan authorities said they have thwarted other large-scale attacks targeting public spaces. Kenyan police said in September 2012 they disrupted a major terrorist attack in its final stages of planning, arresting two people with explosive devices and a cache of weapons and ammunition.
Anti-terror Police Unit boss Boniface Mwaniki said vests found were similar to those used in attacks that killed 76 people in Uganda who gathered to watch the soccer World Cup finals on TV in July 2010. Al-Shabab claimed responsibility for those bombings, saying the attack was in retaliation for Uganda's participation in the African Union's peacekeeping mission in Somalia.