Some 14 million Ethiopians are estimated to be at risk from famine next year because of the failure of crucial rains.
Ethiopia's Minister of State for Information Netsanet Asfaw told Reuters news agency that they did not need to use their neighbour's nearby ports of Assab and Masawa.
"We have no problem with ports... our problem at the moment is that there is not enough food to be transported into the country," she said by telephone from the capital, Addis Ababa.
Landlocked Ethiopia currently relies on ports in Djibouti and Somaliland.
Aid agencies estimate that between 1.5m and 2m tonnes of food will have to be brought into Ethiopia to overcome the current crisis.
Relations
Eritrea made the offer despite hostile relations between the two countries' governments, the legacy of a bloody two-year border war, which began in 1998.
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Eritrea itself is also suffering from the worst drought to hit the country since the mid-1980s with 1.4 million people, roughly half the population, affected by the drought.
Eritrea's two ports of Masawa and Assab were the main ports used by Ethiopia until the war broke out in 1998.
There are good roads from the ports both to the Ethiopian capital, Addis Ababa, and northern Ethiopia.
The port of Assab in the south of Eritrea was used almost exclusively by Ethiopia and since the war, the port has been idle.
During the war, a similar offer was made by Eritrea when Ethiopia was again facing drought, but that was rejected by Ethiopia as a publicity stunt.
The Ethiopian Government has blamed donor fatigue for an inadequate response to the impending crisis.
"The latest reports reaching here from parts of the country warn that people are dying of starvation," the information ministry said in a statement released at the weekend.
"It has become apparent that without swift food aid many people will die," it warned.