The toll in the terror attack at an upscale shopping mall in Kenya's capital Nairobi Saturday has risen to 59, Kenya's Cabinet Secretary Joseph Ole Lenku said Sunday. President Uhuru Kenyatta said the killed included some of his family members.

Lenku, who is in charge of the country's internal security, said the operation was "delicate" as the attackers were still holding hostages in the mall, Xinhua reported.

He made the remarks after the standoff between gunmen and security forces continued for more than 20 hours.

Over 200 people have been injured.

Two Indians, including an eight-year-old boy, the son of a local Indian banker, were among those killed. Four other Indians were injured, an Indian government spokesman said in New Delhi Sunday.

Syed Akbaruddin, spokesperson of the external affairs ministry, said the two killed Indians were 40-year-old Sridhar Natarajan, who belonged to Tamil Nadu, and eight-year-old Paramshu Jain, the son of a Bank of Baroda local branch manager.

"According to the Indian diplomats who are at medical facilities treating those injured in Nairobi attack, 4 Indians injured, 2 others sadly died," Akbaruddin posted on Twitter.

Among the four injured Indians were two women, an adult male and a girl.

The militant group Al Shabaab of Somalia has claimed responsibility for the attack.

More special force personnel have been called in around the popular Westgate shopping mall to back up police and troops trying to end the gostage-taking.

Lenku said there were still people inside the building, where the Kenyan security forces have control of the first and second floors, while gunmen were holding hostages on the third and fourth floors.

The official did not elaborate on the number of hostages holed up in the mall which was frequented mostly by foreigners and rich Kenyans.

According to the latest reports, the slain foreign victims include Canadians, French nationals and a Chinese.

The Kenyan authorities said 10 to 15 attackers were killed in the shootout.

"With the entire nation, I stand with the families of those who have lost their lives and extend every Kenyan's deepest condolences," Kenyatta said said in a televised address late Saturday.

An emotional Kenyatta also confirmed that he lost some of his very close family members.

"I know how you feel, having also personally lost very close family members. I ask god to give all of us comfort as we confront this tragedy," he said.

Al Shabaab said in its Twitter account "HSM Press Office" that "the Mujahideen entered #Westgate Mall today (Saturday) at around noon and are still inside the mall, fighting the #Kenyan Kuffar inside their own turf".

"Since our last contact, the Mujahideen inside the mall confirmed to @HSM_Press that they killed over 100 Kenyan kuffar & battle is ongoing," the group said.

"HSM has on numerous occasions warned the Kenyan government that failure to remove its forces from Somalia would have severe consequences.

"The Kenyan government, however, turned a deaf ear to our repeated warnings and continued to massacre innocent Muslims in Somalia," the group said.

"By land, air and sea, #Kenyan forces invaded our Muslim country, killing hundreds of Muslims in the process and displacing thousands more," the group said.