Kenya's military reported late Sunday that it had rescued hostages and secured "most parts" of an upscale shopping mall in Nairobi where al-Qaeda-linked militants armed with assault rifles and grenades killed scores of people in an attack and two-day siege.
The Red Cross in Kenya said the death toll in the attack at Narobi's Westgate Shopping Mall was at least 68.
The Kenya Defence Forces posted on its Twitter account that "most of the hostages hostages have been rescued'' and that four security forces had taken control of "most parts of the building.''
"All efforts are underway to bring this matter to a speedy conclusion,'' the government's defense forces statement said.
Many of the rescued hostages - mostly adults - were suffering from dehydration, Col. Cyrus Oguna, a military spokesman, told The Associated Press. Oguna refused to release the number of hostages rescued or those still being held. He said some of the attackers had "most probably" been killed in the operation, which began in the morning and culminated in the evening.
Secretary of State John Kerry called the attackers "ruthless and completely reckless terrorists." He spoke Sunday with Somalia's foreign minister and U.N. ambassador.
State Department spokeswoman Marie Harf said five Americans were among the people injured in the attack. She said the U.S. has no reports of any American deaths, although the wife of a Foreign Service employee working for the U.S. Agency for International Development was killed.
Harf said U.S. law enforcement, military and civilian personnel in Nairobi are providing advice and assistance to the Kenyan authorities. She said the U.S. government condemns the "despicable massacre of innocent men, women and children'' at the shopping mall.
An unknown number of extremists and hostages remained in the mall. Kenya's Daily Nation reported that a combination of Kenyan defense and internal security security forces were attempting to make an assault on the attackers, reportedly holed in a room with bulletproof glass.
Earlier, Kenya's interior cabinet secretary Joseph Lenku said 175 were injured and that about 1,000 people have been rescued so far.
The Somali militant group al-Shabaab claimed responsibility on Twitter for Saturday's attack, which was allegedly carried out by 10 to 15 gunmen with AK-47s and other sophisticated weapons. Al-Shabaab, which said the attack was retribution for Kenyan forces' 2011 push into Somalia, threatened more violence.
"The Mujahideen entered #Westgate Mall today at around noon and are still inside the mall, fighting the #Kenyan Kuffar inside their own turf," the group said on Twitter.
"What Kenyans are witnessing at #Westgate is retributive justice for crimes committed by their military," the group said.
On Friday, the day before the attack on the mall began, U.S. Defense Secretary Chuck Hagel hosted the Somalia President Hassan Sheikh Mohamud, senior members of his cabinet, and the chief of the Somali National Army, Gen. Dahir Elmi.
The Pentagon said Hagel "reaffirmed the United States' support to the year-old Federal Government of Somalia and the Somali people" and that Hagel and the Somali leaders discussed how the U.S. military might assist in the training of Somali troops.
President Obama called President Uhuru Kenyatta of Kenya on Sunday to express condolences. Obama "reiterated U.S. support for Kenya's efforts to bring the perpetrators of the attack to justice," the White House said in a statement.
Kenyans and foreigners were among those confirmed dead, including French and Canadians. Kenyatta said he lost some family members in the attack.
The Israeli publication Haaretz was among media reporting that Israeli advisers were aiding Kenyan authorities. All Israelis in the mall had escaped, Haaretz said.
A local organization was hosting a party for children at the Israeli-owned Westgate mall on Saturday. The mall is also a popular nightspot for hip, young Kenyans who gather there to watch movies or eat at restaurants.
Prime Minister David Cameron said three Britons had died in the attack, adding that "we should prepare ourselves for further bad news."
Kenya's presidential office said that one of the attackers was arrested on Saturday and died from bullet wounds. Lenku said there were 10 to 15 attackers involved. He said that Kenyan forces have control of the mall's security cameras.
Kenyan media reported that several people in hiding in the mall escaped to safety.
Cecile Ndwiga said she had been hiding under a car in the basement parking garage.
"I called my husband to ask the soldiers to come and rescue me. Because I couldn't just walk out anyhow. The shootout was all over here - left, right- just gun shots," she said.
Nairobi resident Paolo Abenavoli said he is holed up in his apartment only 100 meters from the mall with a direct view of the entrance. He said he could see a dozen or more security forces inside a first floor restaurant.
"The battle is on now," Abenavoli said by telephone as the fresh gunfire broke out Sunday.
The attack began on Saturday afternoon when gunmen tossed grenades and opened fire as panicking shoppers fled the building, some jumping down one story from the second floor of the mall to escape, witnesses told the Nation.
Witnesses told local and national news media that the gunman asked Muslims to leave before opening fire. Kenya is 83% Christian with a sizable Muslim community - about 11% of its 44 million people.
The gunmen carried AK-47s and wore vests with hand grenades on them, Manish Turohit, 18, who hid in a parking garage for two hours, told the Associated Press.
"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.
Off-duty Sgt. Major Frank Mugungu told AP that he saw four male attackers and one female, and that he could clearly identify one of the gunmen as a Somali, though he could not identify the rest.
Military cordoned off the building in the heart of the upscale Westlands district, which is home to upper-class Kenyans and expatriate Westerners - many of whom work for the United Nations - and a locale frequented by tourists.
It is on Kenya's watch list as a site for attacks, along with its towering conference center and Western hotels such as the Hilton.
Contributing: Jabeen Bhatti from Berlin; the Associated Press