Kenya's interior minister says most of the hostages have been rescued from the Nairobi shopping mall that Islamist militants stormed on Saturday.
Joseph Ole Lenku said Kenyan forces are now in "full control" of the Westgate Mall. He said two gunmen had been killed in the ongoing military operation.
He 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.
The military began an assault on the mall Sunday night. Lenku said 62 people have been killed since gunmen attacked the buildings on Saturday, while the Kenyan Red Cross put the death toll at 69.
The Red Cross says another 175 people have been wounded and at least 65 others are registered as missing.
It was not clear how many hostages were rescued Monday, or how many might remain in the mall.
The Somali terrorist group al-Shabab claimed responsibility for the attack, saying it was in retaliation for Kenya's military intervention in Somalia. 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.