The military says that “most” of the Kenya hostages who have been held at an upscale shopping mall in Kenya’s capital after it was attacked by members of an Al Qaeda-linked Somali militant group on Saturday have been freed.

Kenya’s armed forces launched what was referred to as a “major” assault on the militants on Sunday night, which was about 30 hours after the Islamists stormed the Nairobi mall in an attack that left at least 68 dead and 175 injured. At around midnight local time, Kenya’s Defence Forces said it had rescued most hostages and had taken control of most of the mall, but declined to give numbers. Officials said four Kenyan military personnel were wounded in the operation.

“This will end tonight,” Kenya’s Disaster Operation Center earlier said.

Somalia’s Al Qaeda-linked rebel group, al-Shabab, claimed responsibility for the Saturday attack in which they used grenades and assault rifles and specifically targeted non-Muslims. The rebels said the attack was retribution for Kenyan forces’ 2011 push into Somalia and threatened more attacks.

The announcement of the Kenya military assault came after Associated Press reporters said they heard a large explosion at the mall, followed by silence.

The Kenyan military had remained in a tense standoff with Islamic extremists throughout Sunday, as exchanges of gunfire between both sides were heard inside the mall, Reuters reports.

Kenya’s president, Uhuru Kenyatta, said in a national address Sunday that security forces had managed to isolate the “criminals” in one place inside the building, according to Reuters. Two helicopters were seen flying over the mall.

Many of the rescued hostages — mostly adults — were suffering from dehydration, Col. Cyrus Oguna, a military spokesman, told The Associated Press

There are between 50 to 200 hostages and most of them were hiding in various places inside the mall, Fox News confirms. They are not being held by the hostage-takers. There are between 10 to 15 militants currently inside the mall, with at least one being female.

Some of the people in hiding managed to escape before the military assault, according to Kenyan media reports.

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.

Police said that 49 people had been reported missing, according to a statement released by Kenya’s Red Cross.

Kenyatta said in his address that the attackers “shall not get away with their despicable and beastly acts.”

“We will punish the masterminds swiftly and indeed very painfully,” he added.

The White House said Sunday that President Barack Obama called Kenyatta to tell him the United States supports his country’s effort to bring al-Shabab to justice.

As of Sunday evening local time, Kenya’s Red Cross said 68 people were killed in the violence.

Kenyans and foreigners were among those confirmed dead, including French, Canadians and Chinese. The U.S. State Department said four American citizens were injured and were being given assistance. The age of the victims ranged from 2 to 78, Reuters reports.

Nineteen people, including at least four children, died after being admitted to Nairobi’s MP Shah hospital, said Manoj Shah, the hospital’s chairman. “We have at least two critical patients currently, one with bullets lodged near the spine,” he said.

A statement by Secretary of State John Kerry noted a victim killed in the assault.

“Although we have no reports of any Americans killed today, we have lost a member of our own State Department family: the wife of a foreign service national working for the U.S. Agency for International Development. The men and women of USAID work courageously around the world to help people striving for a better life.  While we mourn with her family today, we also pledge our commitment to do whatever we can to assist in bringing the perpetrators of this abhorrent violence to justice, and to continue our efforts to improve the lives of people across the globe,” the statement said.

Kenya’s presidential office said that one of the attackers was arrested on Saturday and died after suffering from bullet wounds.