Most of the victims were lawyers who had gathered to mourn a prominent local lawyer was had been killed by gunmen earlier on Monday.
The Taliban faction, Jamaat-ul-Ahrar, said it was behind both the hospital attack and the killing of Mr Kasi.
The attack occurred only hours after lawyer Bilal Anwar Kasi, president of the Baluchistan Bar Association, was shot and killed on his way to court. Several lawyers were also targeted during a recent spate of killings in Quetta. The claim could not be independently verified.
This is the largest single attack in Quetta in quite some time. Afridi said most of the dead were lawyers.
In a statement, Ahsanullah Ahsan, spokesman for the Jamaat-ul-Ahrar militant group, said its fighters killed Bilal Kasi, the president of the Baluchistan Bar Association, then as dozens of lawyers gathered at the government-run Civil Hospital, a suicide bomber targeted the mourners.
Many of those killed in the attack were lawyers, The Associated Press reported. He said lawyers across the country will observe three days of mourning and will stay away from court appointments to express solidarity with those killed in the attack.
Television footage showed scenes of chaos, with panicked mourners fleeing through debris as smoke filled the corridors of the hospital's emergency ward.
The blast was so powerful that they both fell down, he said.
The military has been deployed in and around Quetta's hospitals. What goes on in the minds of those who attack public hospitals and unarmed civilians is something one might never know.
Democratic presidential nominee Hillary Clinton today condemned the "despicable" terror attack at a hospital in Pakistans restive balochistan province, saying there was a need to stand up against terror and prevent such assaults.
"It was a suicide attack", said Zahoor Ahmed Afridi, a senior police officer.
63 killed in Pakistani hospital bombing
Pakistan's prime minister has denounced the huge bombing that struck a hospital in the southwestern city of Quetta , killing 30. Pervez Masi, who was injured by pieces of flying glass, said the blast was so powerful that "we didn't know what had happened".
Sanaullah Zehri, the chief minister in Baluchistan province, where Quetta is the capital, says it seemed to be a suicide attack but that the police are still investing.
AP reports: "Prime Minister Nawaz Sharif strongly condemned the blast and expressed his "deep grief and anguish over the loss of precious human lives" in the attack". He also instructed health officials to provide the best treatment possible.
"No one will be allowed to disturb the peace in the province that has been restored thanks to the countless sacrifices by the security forces, police and the people of Baluchistan", he said in a statement.
He had earlier visited the hospital and inquired after the injured victims of Quetta blast.
No one immediately claimed responsibility for the attack.
It is the second deadliest in Pakistan this year so far, after a bombing in a crowded park in Lahore over Easter killed 75.
Abdul Rehman, the director at the Civil Hospital, said the bombing killed 67 people, mostly lawyers.
ARY News said the dead included 25 lawyers and two journalists, including Aaj TV cameraman Shehzad Khan, who could be heard clearly on the camera reciting the "Kalma" in a groaning voice as he died.
Anwar Kakar, the official spokesman for the government of Baluchistan, toldNBC: "This doesn't look like the action of insurgent separatists, rather religious extremists".
Kasi was targeted by two unidentified gunmen, who opened fire on his auto near Quetta's Mengal Chowk.