The decision follows the killing of nearly 90 people in a terror attack Feb. 17 in the Shiite-dominated city in southwestern Pakistan.
Pakistani police arrested 170 suspects in the aftermath of the attack, which targeted a Shiite Muslim area in Quetta. The explosion in a market area killed 89 people, primarily Shiites from the Hazara ethnic group, and injured dozens of others.
Many of Quetta's Hazaras are Afghans who originally fled persecution there. But since their arrival in Pakistan they have repeatedly been targets of indigenous Sunni extremists.
Quetta, the capital of Pakistan's Balochistan province, which borders Iran and Afghanistan, has long been unsettled by both a separatist insurgency as well as sectarian violence.
A spokesman for Ashraf's office said the prime Minister "has ordered an immediate launch of targeted operation aimed at eliminating those responsible for playing with the lives of innocent civilians and restoring peace and security in Quetta," the Deccan Herald reported Tuesday.
It is the second major attack on Quetta's 600,000-person Shiite Hazara community in five weeks.
On Jan. 10, twin suicide bomb attacks at a social center killed at least 92 people and wounded 121.
The banned Sunni militant group Lashkar-e-Jhangvi claimed responsibility for that bombing and has reportedly claimed responsibility for the latest attack.
Ashraf said the operation is aimed at "eliminating those responsible for playing with innocent people's lives."
Imran Khan, former Pakistani cricketer who is chairman of the Pakistan Tehreek-e-Insaf ("Movement for Justice") political party, told a news conference: "I tell you by name, Lashkar-e-Janghvi, I tell you by name that this terrorism that you are carrying out in the name of Islam, there can be no bigger enemy of Islam than you.
"Islam is the name of humanity. What you are doing to a different sect of your own religion is something you should not be doing to atheists. I strongly condemn you. I also strongly condemn you on behalf of the Pakistani nation. And I say that this terrorism, that through this that you are carrying out, you are harming Islam, you are harming Pakistan."
LeJ has carried out suicide bombings and other attacks on Shiite Muslims in a bid to destabilize Pakistan and install a Sunni theocracy. Pakistani analysts say the strategy is similar to that used by al-Qaida to try to trigger a civil war in Iraq several years ago.
Underlining the difficulties of the issue, the Supreme Court has rejected the Balochistan governor's report on the massacre of Hazara community in Quetta and summoned provincial home secretary, inspector general of police and the commandant of the Frontier Corps and the capital city police officer in Quetta to explain the recent unrest.
Pakistani Interior Secretary Rehman Malik said in hearings that the LeJ had accepted the responsibility for the attack. In response, the Chief Justice of Pakistan noted that that the LeJ's liability had been admitted and inquired, "Who is taking action against the culprits?"