Pakistan's prime minister Nawaz Sharif vowed on Monday to hunt down and defeat the militants who have been carrying out attacks like the Easter bombing that targeted Christians and killed 72 people.

"We will not allow them to play with the lives of the people of Pakistan," Mr Sharif said. "This is our resolve. This is the resolve of the 200 million people of Pakistan."

As the country began three days of mourning after Sunday's suicide bombing in the eastern city of Lahore in a park crowded with families, Mr Sharif said the army would forge ahead with a military operation on extremist hideouts and police will go after what he called the "cowards" who carried out the attack.

Jamaat-ul-Ahrar, a breakaway Taliban faction that supports the Islamic State group, claimed responsibility and said it specifically targeted Christians.

But most of those killed were Muslims who also had been in the popular park for the holiday. Many women and children were among the victims, and dozens of families held tearful funerals on Monday for their slain relatives. At least 300 people were wounded.

Mr Sharif, who cancelled a visit to the United States to attend a nuclear summit, also warned extremists against using Islam to justify their violence in the overwhelmingly Muslim nation.

Pakistan has suffered a series of attacks in recent months, and Mr Sharif said militants are hitting "soft targets" like playgrounds and schools because military and police operations are putting pressure on their operations.

Mr Sharif met with security officials earlier in the day, and raids and dozens of arrests were carried out in eastern Punjab province, where several militant organisations are headquartered.

The prime minister also visited hospitals in Lahore where many of the injured were being treated. Mr Sharif was born in the city, which is also the capital of Punjab province, his power base.

"It strengthened my resolve when I met the wounded people," he said in his address. "God willing, I will not sit idle until I bring smiles back on their faces."

The attack underscored both the militants' ability to stage large-scale attacks despite a government offensive and the precarious position of Pakistan's minority Christians.

At the Vatican, Pope Francis decried what he called the vile and abominable bombing against Christians and urged Pakistani authorities to "make every effort to restore security and serenity" in the country, particularly for religious minorities.

In Pakistan's capital of Islamabad, Islamic extremists protested for a second day outside Parliament and other key buildings, demanding that authorities impose Sharia law. The army deployed paramilitary Rangers as well as about 800 additional soldiers from neighbouring Rawalpindi to Islamabad, to protect the centre, which houses main government buildings and diplomatic missions.

The leader of the protesters, Sarwat Ejaz Qadri told a local TV channel they would stay outside Parliament "until our demands are met". Hundreds were hunkered down for a long stay, chanting prayers, occasionally raising anti-government slogans and brandishing long sticks.

They were protesting against the hanging last month of policeman Mumtaz Qadri. He was convicted for the 2011 murder of governor Salman Taseer, who was defending a Christian woman jailed on blasphemy charges. Mr Taseer had also criticised Pakistan's harsh blasphemy laws and campaigned against them. The woman, Aasia Bibi, is still in jail facing blasphemy charges.

In recent weeks, Pakistan's Islamist parties have been threatening widespread demonstration to protest what they say is Mr Sharif's pro-Western stance. They have also denounced draft legislation in Punjab province that outlaws violence against women.

Earlier this month, Mr Sharif had officially recognised holidays celebrated by Pakistan's minority religions, including Easter and the Hindu festival of Holi.

Ahsanullah Ahsan, a spokesman for the breakaway Taliban faction, said that along with striking at Christians celebrating Easter, the bombing also was meant to protest against military operations in the tribal regions. The same militant group also took responsibility for the twin bombings of a Christian church in Lahore last year.

But of the 72 dead from Sunday's attack, 14 have been identified as Christians and 44 as Muslim, said Lahore Police Superintendent Mohammed Iqbal. The rest have not been identified.

Shama Pervez, a widow who lost her 11-year-old son Sahil in the bombing, was inconsolable at his funeral. A fifth-grader at a Catholic school, he had pleaded with her to go to the park rather than stay home on Sunday, and she said she finally gave in.

In the Christian area of Youhanabad on the outskirts of Lahore, mourners crowded into a church that was targeted in an attack a year ago.

"How long will we have to go on burying our children?" asked Aerial Masih, the uncle of Junaid Yousaf, one of Sunday's victims.

Ten members of Qasim Ali's family were killed in the park, and all were Muslims. His 10-year-old nephew, Fahad Ali, lay wounded in a bed at home. He had lost his parents and a sister, and another two sisters also were badly injured.

"I don't know how I will be able to do anything to continue at school!" he cried.

Forensic experts searched debris in the park. The bomb had been a crude device loaded with ball bearings, designed to rip through the victims for maximum damage, said counter-terrorism official Rana Tufail. He identified the suicide bomber as Mohammed Yusuf, a known militant recruiter.

Nobel peace prize laureate Malala Yousafzai, herself a survivor of a Taliban shooting, said she was "devastated by the senseless killing of innocent people in Lahore."

"My heart goes out to the victims and their families and friends," she said. "Every life is precious and must be respected and protected."

White House spokesman Josh Earnest called the bombing "grotesque."

"The fact that you have an extremist organisation targeting religious minorities and children is an outrage," he said, also noting the high number of Muslims among the victims.

Turkish president Recep Tayyip Erdogan said targeting a park filled with children "revealed the face of terror, which knows no limits and values".

France expressed its "solidarity in these difficult moments" with Pakistan and underlined "the inflexible will of our country to continue to battle terrorism everywhere".

Zahid Hussain, an expert on Pakistani militants, said the violence was a show of strength by religious extremists, angered over what they see as efforts to undermine their influence.

Pakistan's military launched an all-out offensive against militants in the North Waziristan tribal region bordering Afghanistan in June 2014. The army says the operation, called Zarb-e-Azb, has killed more than 3,000 militants. In December 2014, the Taliban retaliated with one of the worst terror assaults in Pakistan, attacking a school in north western city of Peshawar and killing 150 people, mainly children.

Mr Hussain said the government has sent mixed signals to Islamic extremists. On one hand, it has allowed banned radical groups to operate unhindered under new names and radical leaders to openly give inciting speeches. At the same time, it has hanged convicts like Qadri and promised to tackle honour killings and attacks against women.

"It is one step forward and two steps backward," Mr Hussain said. "The political leadership has to assert itself and say no to extremism once and for all."

Army chief General Raheel Sharif promised Pakistan "will never allow these savage non-humans to overrun our life and liberty".

Punjab's government said it will give about 3,000 US dollars in compensation to the seriously wounded and 1,500 US dollars to those with minor injuries from the bombing.