At least 11 people died in Saturday's fighting, said Ajdabiya hospital supervisor Mohammed Idris, with two more rebels killed Sunday.
Shelling and gunfire was heard across the city as forces loyal to Moammar Gadhafi and rebels battled. It's the most serious push into rebel-held territory since international airstrikes began.
Recapturing Ajdabiya would give Gadhafi's forces a staging ground to move on Benghazi, the rebels' main stronghold.
NATO warplanes are continuing to bombard Gadhafi's ammunition stockpiles and armored forces. Rebels have criticized the NATO for not giving them sufficient battlefield support as government forces continue to push into the east.
In Cairo, a Red Cross shipment of 1,100 pounds (500 kilograms) of medicine and health care equipment left for the Libyan border to aid Libyan refugees.
The Associated Press contributed to this report.