Renewed fighting in the city had already slowed bids to bring in relief supplies.
The Syrian Red Crescent said its vehicles were fired on, and that one of its drivers was wounded.
However, Syrian state media said four Red Crescent aid workers were wounded by rebel gunfire.
The UN is overseeing efforts to deliver food, water and medicine by truck to some 3,000 civilians in rebel-held areas.
The government and rebels accused each other of violating a ceasefire after mortar fire on Saturday morning delayed an earlier attempt to bring in aid.
On Friday, the first day of the agreed three-day ceasefire, more than 80 children, women and elderly people were evacuated.
Many of those evacuated on Friday looked frail and described extreme hardships inside the area, which has been under army siege for nearly a year-and-a-half.
They said bread had not been available for months, and many residents were gathering weeds and leaves to eat.
Relief officials had earlier warned that this second phase of the humanitarian operation, to allow aid into the embattled quarter, was particularly delicate, not least because the government side has always been reluctant to see supplies going in to rebel-held areas.
If the aid does reach the city, the next step would be another day of evacuations.
During Friday’s operation, vulnerable civilians such as children, old people and medical cases were brought out of the besieged area, sometimes carried by Red Crescent volunteers.
They told journalists that there were more people trapped in the city who had wanted to leave.
Homs has been a key battleground in the uprising against President Bashar al-Assad.
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