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 The Associated Press 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 and that the official civilian death toll remains 61.
"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. Estimates varied between only a few bodies to dozens of bodies possibly still inside the mall.
Photos and video of the damage showed 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.
The United States Ambassador to Kenya says U.S. experts are helping Kenyan forces search for bodies and evidence in the collapsed mall that Islamic terrorists held for four days.
Robert F. Godec said in a statement Wednesday that the U.S. is providing technical support and equipment to Kenyan security forces and medical responders.
Godec said, at the request of the Kenyan government, the U.S. is assisting the investigation to bring the attack's organizers and perpetrators to justice.
Kenyan forensic experts - aided by American FBI agents and Israeli specialists - are working to reconstruct what happened in the attack, said Esipisu, speaking at the mall scene Wednesday. British forensic experts are also expected.
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 about the attack, 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.
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.
The Westgate Mall, which was popular with foreign residents of the capital as well as tourists and wealthy Kenyans, is now being treated as a crime scene and the Kenyan military has handed over control of the building to the police.
President Uhuru Kenyatta told the nation Tuesday night that the terrorists had been defeated and declared three days of national mourning beginning Wednesday.
Early Wednesday morning, occasional gunshots could still be heard from the mall. Esipisu said they were from Kenyan forces going room to room in the large Westgate Mall, firing protectively before entering unknown territory.
"During sanitization once you take control of the place if you go to a room where you haven't visited before you shoot first to make sure you aren't walking into an ambush," he said. "But there hasn't been any gunfire from the terrorists for more than 36 hours."
The attack claimed by Somali militant group al-Shabab killed at least 61 civilians, six security officers and five extremists, the president said.
Another 175 people were injured, including more than 60 who remain hospitalized.
Fears persisted that some of the attackers could still be alive and loose inside the rubble of the mall, a vast complex that had shops for retailers like Bose, Nike and Adidas, as well as banks, restaurants and a casino.
A high-ranking security official involved in the investigations said it would take time to search the whole mall before declaring that the terrorist threat had been crushed. That official insisted on anonymity in order to discuss information not publicly disclosed.
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 al-Shabab extremists stormed the mall on Saturday, throwing grenades and firing on civilians.
The group used Twitter to say that Somalis have been suffering at the hands of Kenyan military operations in Kenya, and the mall attack was revenge.
"You could have avoided all this and lived your lives with relative safety," the group Tweeted Tuesday. "Remove your forces from our country and peace will come."
The militants specifically targeted non-Muslims, and at least 18 foreigners were among the dead, including six Britons, as well as citizens from France, Canada, the Netherlands, Australia, Peru, India, Ghana, South Africa and China. Five Americans were among the wounded.
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.
Associated Press writer Tom Odula contributed to this story.