Afghan President Hamid Karzai has summoned his security chiefs for an emergency meeting to brief him about Tuesday's suicide attacknear a Shia shrine in the capital, Kabul.
Later on Wednesday, Karzai, who cancelled a visit to the UK to return home after this week's Bonn conference, will visit a hospital in the city where dozens of people injured in the bombing are being treated, his spokesman Aimal Faizi said.
At least 56 people were killed in a blast in Kabul on the Shia holy day of Ashoura. A second near-simultaneous strike killed four people and injured 21 in the northern city of Mazar-e-Sharif as a convoy of Shias was driving past.
It was not immediately clear who carried out the attacks but suspicion centred on Sunni armed groups based in neighbouring Pakistan.
"Without any doubt, the enemies of Afghanistan are trying to separate the Afghan people," Karzai said in a statement.
He did not blame any specific group, but when he uses the phrase "enemies of Afghanistan," it is widely believed that he is referring to countries, including Pakistan, that he suspects are backing fighters in Afghanistan.
Until now, the decade-long Afghan war has largely been spared sectarian violence.
Burying the dead
Meanwhile, families gathered for funerals across the city of Kabul on Wednesday.
In western Kabul, a group of mourners carried four bodies in a funeral procession through the city's largest Shia cemetery. They also carried pictures of the dead and shouted, "They are martyrs! We honor them!"
One of the mourners said no place felt safe anymore.
"Killing Muslims in front of a holy shrine, it is unbelievable," said Mohammad Nahim, 35. "Last night I told my children not to visit any shrines after dark. It is too dangerous."
He said the graphic images of piled bodies came on the television as his family was eating dinner the night before and they all started crying.
Rahmaz Ali, a Shia elder in Kabul, said: "This was not Afghan. They [the attackers] were from outside. Sunni and Shia in Afghanistan are like brothers."
Afghanistan's Shia community of mostly ethnic Hazaras make up about 20 per cent of the nation's 30 million population.
The attacks werer condemned by the Taliban, which has waged a decade-long fight against Afghan forces and its NATO-led coalition allies.
"Very sadly we heard that there were explosions in Kabul and Mazar-e-Sharif, where people were killed by the enemy's un-Islamic and inhuman activity," Zabihullah Mujahid said in a statement published on the group's website.
The US also condemned the attacks and vowed not to let the country regress into extremism, with Secretary of State Hillary Clinton calling the bombings "deplorable."
"Those responsible show their complete disregard for the efforts of the Afghan people to make their country more stable, more peaceful and more democratic," she said in a statement.
"The United States will continue to work with the Afghan government and people to combat violent extremism and continue progress toward a peaceful, democratic and prosperous Afghanistan.
Kabul has been targeted by a series of bold attacks in recent months; include assaults on the US embassy, a major hotel and the offices of the British Council.