The Taliban-claimed attack -- the second carried out by the militant group in the Afghan capital in a week -- also wounded 158 people, in one of the biggest blasts to rock the war-torn city in recent years.
"All countries who support peace in Afghanistan have an obligation to take decisive action to stop the Taliban's campaign of violence. There can be no tolerance for those who support or offer sanctuary to terrorist groups," Tillerson said in a strongly worded statement.
Tillerson's strong statement though made no mention of Pakistan.
The United States strongly condemns "today's horrific attack" in Kabul, he said.
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"Our thoughts are with the families of the victims who were injured and killed, and we mourn all those who lost their lives in this senseless attack," he added.
"The Taliban's use of an ambulance as a weapon to target civilians represents inhumane disregard for the people of Afghanistan and all those working to bring peace to the country, and is a violation of the most basic international norms," Tillerson said.
Commander of US and NATO forces in Afghanistan Army Gen John W Nicholson said that the attack once again demonstrates that the enemies of Afghanistan kill indiscriminately.
"Unarmed civilians throughout Afghanistan regularly bear the brunt of this cruelty," he said.
"As our thoughts turn to the family and friends of those killed and injured at this time, we will also go forward and do our best work in their memory -- defeating the insurgents and bringing peace to this region," Nicholson said.