Rice's November 2014 death at the hands of a white officer in the US state of Ohio shocked Americans and the $500 bill sent to his family has only stoked further outrage.
"Asking Tamir's family to pay for his ambulance is heartless. Cleveland should drop this fee," Democratic presidential candidate Hillary Clinton said on Twitter.
Local media reported that lawyers for the Rice family said the bill only added "insult to homicide."
Asking Tamir's family to pay for his ambulance is heartless. Cleveland should drop this fee. https://t.co/Gq8twYI1QD -H- Hillary Clinton (@HillaryClinton) February 11, 2016
Faced with the snowballing controversy, Mayor Frank Jackson called a news conference on Thursday during which he admitted a mistake had been made.
"We will start off again apologizing to the Rice family if this has added to any grief or pain they may have" he said, surrounded by other city leaders.
Together they explained that the bill was sent under routine procedure and that it was meant for the boy's insurance company, not his family.
Surveillance video showed Rice was fatally shot within seconds of a patrol car arriving on the scene as he began to pull the toy gun out of his waistband. The boy died hours later in hospital.
The shooting followed a series of high-profile incidents of police violence involving black Americans and helped fuel protests against what some say is white police impunity despite discrimination against blacks.
In December, a grand jury declined to bring criminal charges against the Cleveland police officers involved in the fatal shooting.