Al-Shabab on its Twitter feed Wednesday claimed that the Kenyan government assault team carried out "a demolition" of the building.
The current death toll is 67 and is likely to climb with uncounted bodies remaining in the wreckage of the Nairobi mall. Another 175 people were injured, including more than 60 who remain hospitalized. At least 18 foreigners were among those killed.
Al-Shabab, the Somali Islamic extremist group which carried out the attack, said Wednesday that foreigners were a "legitimate target" and confirmed witness accounts that gunmen separated Muslims from other people and let the Muslims go free. The others were gunned down or taken hostage.
"The Mujahideen carried out a meticulous vetting process at the mall and have taken every possible precaution to separate the Muslims from the Kuffar (disbelievers) before carrying out their attack," the group said in an email exchange with The Associated Press.
Witnesses have told AP and other media that gunmen rounded up people, asked questions about Islam that a Muslim would know and told the Muslims to leave the mall. Still, some Muslims were among the victims.
Also among those killed when the militants entered the Westgate Mall on Saturday, firing assault rifles and throwing grenades were six Britons and citizens from France, Canada, the Netherlands, Australia, Peru, India, Ghana, South Africa and China.
Asked if al-Shabab had intended to kill foreigners, the group said "our target was to attack the Kenyan govt on it's soil and any part of the Kenyan territory is a legitimate target ... and Kenya should be held responsible for the loss of life, whether foreigners or local."
Al-Shabab had threatened retaliation against Kenya for sending its troops into Somalia against al-Shabab, and many of those killed in an attack that horrified the world were Kenyans. The group's leader, Ahmed Godane, said in a new audio statement Wednesday that the attack was carried out in retaliation for the West's support for Kenya's Somalia invasion and the "interest of their oil companies." Somalia has untapped energy reserves. More attacks would come, Godane said, if Kenya doesn't withdraw its troops.
Though Kenya's foreign minister earlier said that "two or three" American citizens may have been involved in the attack, a Western official said that after checking passport and refugee databases, there is not yet an indication any Americans were involved. Several U.S. cities, notably Minneapolis, host large Somali-American communities.
The violence continued elsewhere Wednesday. In the Kenyan town of Wajir, which lies along the border with Somalia, one person was killed and four wounded after a gunman opened fire and threw grenades, the Interior Ministry said.
Interior Minister Joseph Ole Lenku said forensic experts from the U.S., Israel, Britain, Germany and Canada are all taking part in trying to reconstruct the scene at the mall. He said results would not be ready before a week's time.
Morgue officials in Nairobi have been prepared for the last two days for a large influx of bodies still in the mall. Officials have told AP that the shopping center, which the terrorists held for four days, could hold dozens more bodies. The government has confirmed 72 total deaths: 61 civilians, six security forces and five attackers. The Red Cross says 71 people remain missing.
Al-Shabab said the Kenyan government assault team carried out "a demolition" of the building, burying 137 hostages in the debris. A government spokesman denied the claim and said Kenyan forces were clearing all rooms Wednesday, firing as they moved and encountering no one.
The al-Shabab claim appeared to refer to the rocket-propelled grenades fired inside the Nakumatt department store, in the incident described to AP by a government official.
In a series of tweets from a Twitter account believed to be genuine, al-Shabab also said that "having failed to defeat the mujahideen inside the mall, the Kenyan govt disseminated chemical gases to end the siege."
Kenyan government spokesman Manoah Esipisu told AP that no chemical weapons were used including tear gas and that the collapse of floors in the mall was caused by a fire set by the terrorists.
"Al-Shabab is known for wild allegations and there is absolutely no truth to what they're saying," he said. But officials said the death count will likely rise.
The country's interior minister in a press conference said an "inconsequential number" of bodies remained in the mall.
The mall's top level parking lot collapsed in the middle of the building. That brought the second level down onto the ground floor on top of at least eight civilians and one or more attackers, said Esipisu.
Lenku said there were no indications that a woman took part in the attack, despite persistent press speculation, and he said officials have not yet confirmed reports that the attackers had rented a shop inside the mall.
U.S. Ambassador Robert Godec said Wednesday that Washington is providing technical support and equipment to Kenyan security forces and medical responders. Godec said the U.S. is assisting the investigation to bring the attack's organizers and perpetrators to justice.
In another development, a British man was arrested in Kenya following the terrorist attack, Britain's Foreign Office said.
British officials are ready to provide assistance to the man, the agency said in a statement Wednesday. Officials would not provide his name or details. He is believed to be in his 30s. Britain's Daily Mail newspaper said he was arrested Monday as he tried to board a flight from Nairobi to Turkey with a bruised face and while acting suspiciously.
Kenyan officials have said that 11 suspects in total have been arrested in connection with the attack, including at least seven at the airport. They are being questioned, said the government spokesman.
The International Criminal Court in the Hague has said it is prepared to work with Kenya to bring the attackers to justice. ICC Prosecutor Fatou Bensouda said in a statement that while Kenya has primary jurisdiction in the slaying of civilians in the Westgate Mall, the atrocity could also fall under the court's jurisdiction.
Al-Shabab, whose name means "The Youth" in Arabic, first began threatening Kenya with a major terror attack in late 2011, after Kenya sent troops into Somalia following a spate of kidnappings of Westerners inside Kenya.
The mall attack was the deadliest terrorist attack in Kenya since the 1998 al-Qaida truck bombing of the U.S. Embassy in Nairobi, which killed more than 200 people.
Selsky reported from Johannesburg. Associated Press writers Rodney Muhumuza and David Rising contributed.