Barrazi later told Syrian state TV that two trucks were able to reach opposition-held neighborhoods earlier in the day. Al-Mayadeen also reported that two trucks, carrying the food parcels, were able to cross into rebel-held areas Saturday.
The state TV said four members of the Syrian Arab Red Crescent were wounded by rebel fire in the area but gave no further details.
The Syrian Arab Red Crescent said on its Facebook page that its members were able to deliver 250 food parcels and 190 parcels containing detergents and medicines to the central neighborhood of Hamidiyeh despite being targeted by several mortar rounds. It added that one of its members was lightly wounded and two trucks were damaged. It was not immediately clear why state media said four paramedics were wounded, but the Red Crescent said only one.
Barrazi said about 100 civilians who were expected to be evacuated from rebel-held areas had yet to arrive. On Friday, 83 children, women and elderly people on wheelchairs were evacuated from Homs, the first people to leave the area in months, the U.N. said.
Syrian forces loyal to President Bashar Assad have prevented the entry of food and medical aid into rebel-held parts of the city for more than a year, badly affecting hundreds of civilians holed up in the areas. An agreement had called for a three-day truce to allow the evacuation of some civilians and the entry of food shipments.
Al-Mayadeen aired live footage from the city's Clock Square showing two white trucks identified with Syrian Arab Red Crescent markings as they returned from their unfulfilled mission. The station's reporter in the area said the radiator of one of the trucks was hit by a bullet.
"After the vehicles drove about 200 yards two roadside bombs went off, and when they kept going a mortar round fell in the area coming from the direction of Hamadiyeh," said Barrazi, referring to a rebel-held central neighborhood.
Earlier in the day, a Syrian official said fighting had broken out and that a mortar shell had landed near U.N. personnel. An activist said combat began when government forces fired 11 rockets toward the rebel-held Hamidiyeh quarter. The official spoke on condition of anonymity.
Homs city was one of the first areas to rise up against Assad in 2011 and has been particularly hard hit by the war. Over the past year, the government has regained control over much of the city, except for a few neighborhoods in the historic center.