"I am deeply disappointed that the three-day humanitarian pause agreed between the parties to the conflict was broken today and aid workers deliberately targeted," Amos said in a statement on Saturday.
"Today's events serve as a stark reminder of the dangers that civilians and aid workers face every day across Syria," she said.
Saturday's attack threatened a United Nations-led operation to bring food and medicine to 2,500 people in Homs and evacuate civilians trapped by months of fighting in the Syrian city.
Syrian state television said four members of the Syrian Arab Red Crescent were wounded by militants on Saturday as the aid workers tried to deliver humanitarian supplies to Homs.
It said the Red Crescent members came under fire from armed terrorist groups. There was no immediate comment from militants or opposition groups.
The humanitarian convoy had been delayed since Saturday morning by mortar fire in Homs, which the two warring sides blamed each other for, in violation of a three-day ceasefire for civilians to leave central Homs and aid supplies to get in.
The Red Crescent said on its Twitter feed that an aid truck driver had been wounded after shots were fired at the convoy, and that mortar shells also landed close by as the vehicles moved into the Old City.
It posted a picture which appeared to show a bullet hole in the back window of a Red Crescent car.
Syrian television quoted the governor of Homs, Talal al-Barazi, as saying two cars carrying aid supplies had entered the Old City but that militants had targeted the route with mortar fire, preventing any more vehicles from entering.
Syria has been gripped by deadly unrest since 2011. More than 130,000 people have been killed and millions of others displaced in the violence.
According to reports, Western powers and their regional allies, especially Qatar, Saudi Arabia, and Turkey, support the militants operating inside Syria.
NTJ/HH