Describing the attack in Kabul as "horrifying", he said the deliberate targeting of civilians constitutes a grave violation of human rights and international humanitarian law and "may constitute a war crime".
At least 26 people were killed and 41 injured after a Taliban-claimed car bomb struck a bus carrying government officials through a Shiite neighbourhood in Kabul yesterday.
Guterres also condemned the terrorist attack in Lahore, calling for those responsible to be brought to justice.
The UN chief said that he supports the efforts of the Pakistan government to fight terrorism and violent extremism with full respect for international human rights norms and obligations.
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Lahore police chief Capt (R) Amin Wains confirmed that it was a suicide attack and the "target was police".
Meanwhile, the 15-nation Security Council also strongly condemned both the terror attacks, calling them "heinous and cowardly".
The Council members reaffirmed that terrorism in all its forms and manifestations constitutes one of the most serious threats to international peace and security.
A senior official from the UN Mission in Afghanistan called the attack "cowardly".
"I am personally outraged by all attacks against civilians," said Pernille Kardel, the UN Secretary-General's Deputy Special Representative for Afghanistan.
"The detonation of another large suicide device in a busy, civilian-populated area is egregious, cowardly and bereft of humanity," Kardel said.
The Kabul attack came amid planned commemorations for the July 2016 Dehmazang square attack which claimed the lives of hundreds of people, many from the so-called Enlightened Movement, a coalition of civil society activities, protesting for Hazara minority rights.
"In the context of so much suffering and death, I wish to commend members of the Enlightenment Movement for choosing to address their grievances resulting from last year's attack through dialogue, not violence," said Kardel, who is the acting chief of UNAMA.