"The Tehreek-e-Taliban Pakistan Jamaat-ur-Ahrar takes responsibility for this attack, and pledges to continue carrying out such attacks". It is the second deadliest in Pakistan this year so far, after a bombing in a crowded park in Lahore over Easter killed 75.
There was no independent confirmation of the claim.
Quetta is the capital of southwestern Baluchistan province, which has always been hit by insurgency.
At least 46 dead bodies were taken in to Quetta's Civil Hospital, the clinic that was bombed, Police surgeon Noor Baloch told dpa.
Reports said that majority of those killed and injured were lawyers. A loud explosion was heard at the emergency department where Kasi's body was brought for an autopsy.
The Islamic State claims it was responsible for a suicide bombing that killed at least 70 people at a hospital in Pakistan. A Pakistani news channel reported that one of its cameramen was also killed in the blast. Waliur Rehman said he was taking his ailing father to the emergency ward when the explosion shook the building, knocking them both to the ground.
"Our hearts go out to the families and other loved ones of more than 60 killed and we wish a speedy recovery to the dozens more injured".
Television footage showed scenes of chaos at the hospital in Quetta, with panicked people fleeing through debris as smoke filled the corridors.
"His Holiness Pope Francis sends heartfelt condolences to the relatives of the deceased, to the authorities and to the entire nation, as he offers the assurance of his prayers for the many injured victims of this senseless and brutal act of violence", the statement said.
While Prime Minister Nawaz Sharif expressed his "deep grief and anguish" over the killing, lawyers and journalists held protest demonstrations across several cities.
"No one will be allowed to disrupt the peace of the province", Sharif said.
Chief Secretary Balochistan Saifullah Chatha briefed the Prime Minister on the situation.
Earlier, Pakistan's powerful army chief Gen. Raheel Sharif also visited the hospital, and met with the wounded.
The motive behind Monday's attacks, however, was unclear.
Senior attorney Mohammad Ashraf said on Tuesday that lawyers will also stage rallies across Pakistan to condemn the assault.
Earlier, the Supreme Court Bar Association announced a week-long mourning over the attack.