Nkaissery told reporters the university will be able to confirm Saturday if everyone has been accounted for.
Thursday's attack by al-Shabaab militants killed 147 people, including 142 students, three security officers and two university security personnel. The attack left 104 people injured, including 19 who are in critical condition, Nkaissery said.
During search and recovery efforts on Friday, CNN witnessed one male who was not a student hiding under a bed. That male was taken into custody and was being treated as a suspect, sources close to the search told CNN.
The find sparked an additional search of the building. Sources said three people, all students, were found alive. A female student was found under a pile of bodies, another female student was hiding in a wardrobe and a male student was hiding in the bathroom, the sources confirmed to CNN.
Student Hellen Titus said she survived by fooling the attackers into thinking she was dead.
After gunmen shot fellow students, she smeared their blood onto her body to make it seem she'd been shot, too, she told CNN on Friday at a makeshift center for evacuated students.
"In the time of shooting," she said, "they skipped me."
Most of the victims had been shot from behind, in the back of the head, a medic told CNN.
"They're facing down, always," a worker with St. John's ambulance service said Friday. "They're always facing down, and they're shot in the heads, around the back."
Early Thursday, an explosion and gunfire cut through the morning quiet on the campus about 90 miles (145 kilometers) from Kenya's border with Somalia, tearing many students in dormitories out of their sleep.
"Never heard anything like this," journalist Dennis Okari from CNN affiliate NTV tweeted as he watched smoke rising over a student hostel.
Al-Shabaab gunmen had first stormed a Christian prayer service, where they killed some and took others hostage. Then they went across campus with them, shooting non-Muslims and sparing Muslims, a witness said.
They headed for the hostels.
Student Japhet Mwala lay in her bed. "We were sleeping when we heard a loud explosion that was followed by gunshots, and everyone started running for safety," she told Agence France-Presse.
"There are those who were not able to leave the hostels where the gunmen headed and started firing. I am lucky to be alive because I jumped through the fence with other students," she said.
Students ran -- some crawled -- away from the gunfire, Okari said. At one point, the gunmen pinned down a building where 360 students lived, Interior Minister Joseph Nkaissery said.
Okari took cover outside the campus and listened to explosions and gunfire for four hours. Kenyan security forces moved in and killed four gunmen.
Somali terror group Al-Shabaab, an al Qaeda affiliate, claimed responsibility for the attack.
The Interior Ministry has posted a "most wanted" notice for a man in connection with it. It offered a reward of 20 million Kenyan shillings, about $215,000, for Mohamed Mohamud, who goes by the aliases Dulyadin and Gamadhere.
The post does not say what role the man may have played.
Kenyan police are circulating "Wanted Dead or Alive" posters featuring eight terror suspects who are wanted in separate attacks in Kenya, the Interior Ministry said. Police are offering a bounty of more than $210,000 for the suspects, the Ministry said via Twitter.
The dangerously porous border between Somalia
and Kenya has made it easy for Al-Shabaab militants to cross over and carry out attacks.
In a December attack at a quarry
, Al-Shabaab militants separated Muslims from others and executed the non-Muslims, killing at least 36 people. In November, militants stopped a bus near the border and killed 28 people they believed to be non-Muslims.
Last month, the U.S. Embassy warned of possible attacks "throughout Kenya in the near-term" after the reported death of a key Al-Shabaab leader, Adan Garaar, who was suspected in the September 2013 Westgate Mall attack in Nairobi.
The security question
Police have declared a curfew for the next several days in the region from 6:30 p.m. to 6:30 a.m. The Education Ministry has closed the university indefinitely.
Surviving students have gathered in large groups at the town's airport, waiting to be flown to their hometowns.
The effects are also being felt 225 miles west in Kenya's capital of Nairobi, where the new bloodshed reinvigorated an old debate: Is the nation's security strong enough?
Many thought measures taken after the Westgate Mall massacre had filled the gaps.
At least 67 people died then. But Thursday's attack is the second-worst in the country's history, and it has evaporated much of the confidence won after Westgate. Civil liberty concerns had held up the enrollment of 10,000 new police recruits, but on Thursday, Kenyan President Uhuru Kenyatta gave a directive to process them.
"Kenya badly needs additional officers," he said, "and I will not keep the nation waiting."