"We were sleeping when terrorists attacked the center," said Asif Hussain, a cadet who was in the academy's barracks at the time.
He said the cadets had no guns and were powerless to fight back when the militants struck through the window.
Sarfraz Bugti, home minister for Balochistan province, said three attackers were killed during the assault in Quetta, which targeted a hostel at the academy where hundreds of police recruits were sleeping.
During the hours-long operation that followed, security forces killed one attacker, while two others died when they detonated the bombs they were carrying, he said.
At least 260 cadets were rescued during the operation, which lasted through early Tuesday, he said.
Three days of mourning have been announced in Balochistan province for the dozens of dead, most of whom were police cadets.
Safar Khan, a 24-year-old cadet who was inside his barracks when gunshots rang out, told CNN the survivors refused to be intimidated.
"We will not bow down before terrorists," he said.
ISIS claims responsibility
ISIS released a claim of responsibility for the attack via its Amaq media wing, including a photo of the three purported attackers.
But Maj. Gen. Sher Afgan, chief of the paramilitary Frontier Corps, had earlier told reporters that military officials believed Pakistan-based group Lashkar-e-Jhangvi
was behind the attack.
The al Qaeda-linked militant group has repeatedly carried out deadly terror attacks targeting the country's Shiite Muslim minority in recent years, although it has not issued a claim of responsibility over the latest attack.
Anwar ul Haq Kakar, spokesman for Balochistan province's government, said ISIS' claim of responsibility was being investigated and officials would comment once its inquiries were complete.
In September, Pakistan's military acknowledged for the first time that ISIS had a presence in the country but said it had apprehended hundreds of militants, including the group's core, and prevented members from carrying out major attacks.
ISIS has previously claimed responsibility for a devastating terror attack in Quetta
in August, which was also claimed by Jamaat-ul-Ahrar, a splinter group of Pakistan's Tehreek-i Taliban
Lashkar-e-Jhangvi is known for targeting Shiites in Sunni-majority Pakistan, including a series of bombings in early 2013
that left more than 160 people dead in Balochistan,
the volatile province in southwest Pakistan that borders Afghanistan and Iran.
Last year, the group's leader, Malik Ishaq, was killed during a shootout
after armed men on motorcycles ambushed a police convoy transporting him between prisons in Punjab province.
Laskhar-e Jhangvi also claimed responsibility for a January 2014 bombing of a bus carrying Shiite pilgrims that killed more than 20 people.
Pakistan outlawed the group in 2001, and the US State Department designated it as a terrorist organization two years later.
The police college, on the outskirts of Quetta, has been struck twice before by militants, in 2006 and 2008.
The attack was the latest atrocity to strike the city, which Pakistani Prime Minister Nawaz Sharif and Chief of Army Staff Gen. Raheel Sharif visited on Tuesday.
More than 72 people were killed in an August bombing in Quetta that was one of Pakistan's deadliest attacks.
Gunmen killed prominent lawyer Bilal Kasi, president of the Balochistan Bar Association, before a bomb targeted mourners gathered at the hospital where his body was taken.
"No one will be allowed to disturb peace in the province that has been restored due to countless sacrifices of security forces, police and the people of Balochistan," the Prime Minister said at the time.
Sharif said he had directed authorities to "maintain utmost vigilance."
Militants have targeted educational institutions in the country, especially those linked to state security forces.
In the country's worst terror attack in December 2014, Tehreek-i Taliban militants attacked the Army Public School
in the northwestern city of Peshawar, massacring more than 140 people, most of them children.