Kenya says only a few hostages remain inside the Nairobi shopping mall stormed by Islamist militants Saturday. Dozens of people have been killed in the attack.
The Somali terrorist group al-Shabab claimed responsibility for the assault -- saying it was in retaliation for Kenya's military intervention in Somalia.
Kenyan forces began an assault on the Westgate Mall late Sunday to rescue people hiding from or held captive by the gunmen.
Interior Minister Joseph Ole Lenku told a news conference Monday that Kenyan forces now control every floor of the mall and have rescued most of the remaining hostages.
He said two gunmen had been killed in the ongoing military operation, and 10 members of the security forces wounded.
Lenku spoke about 90 minutes after witnesses heard several large explosions coming from the mall, followed by the sound of gunfire. A column of thick, black smoke continued to rise from the mall after the blasts. Lenku said the militants set mattresses on fire as a distraction.
He said 62 people have been killed since the assault began Saturday. The Kenyan Red Cross put the death toll at 69, with 175 people wounded and at least 65 missing.
An al-Shabab spokesman said in an audio message, "Either leave our country or live with constant attacks."
Kenyan forces entered Somalia two years ago to fight al-Shabab militants who often had crossed the border to stage attacks.
President Uhuru Kenyatta has vowed to stand firm against the threat of terrorism and punish those behind the attack "swiftly" and "very painfully."
The president said Sunday that his nephew and his nephew's fiancee were among those killed in the attack, and that he feels the pain of every life that was lost.
U.S. Secretary of State John Kerry spoke with his Kenyan counterpart Sunday. Kerry called the attack "an enormous offense against everybody's sense of right and wrong.''
The U.N. Security Council and Secretary-General Ban Ki-moon also strongly condemned the attack. Mr. Ban called it a "premeditated" and "totally reprehensible" act targeting defenseless civilians.
Among those killed in the attack were three British nationals, as well as nationals from France, Canada, China, India and South Korea. The United States says no Americans were killed, but that some have been wounded.
President Barack Obama called President Kenyatta Sunday to express his condolences and reaffirm the U.S. commitment to Kenya on fighting terrorism.