Last week, Ban's spokesman said that the secretary-general was concerned by the "aerial bombardments the [Sudanese] government has conducted in several areas of north Darfur".
Ban flew into Addis Ababa from the Democratic Republic of Congo where he had made a keynote speech to the country's parliament.
Mark Sneddon, reporting for Al Jazeera's from Addis Ababa, said that Ban would ask el-Beshir to "go ahead with his commitments" in Darfur.
He said: "Ban Ki-Moon, the quiet man, has been quite steely. He's come to Ethiopia with a pretty strong message for the Sudanese."
The AU summit in Addis Ababa is intended to cover a range of issues from regional security to climate change, with an address from Sir Nicholas Stern, author of a UK government report on the consequences for Africa of global warming.
Sepp Blatter, the president of the International Federation of Association Football (Fifa), is also in Addis Ababa to meet Thabo Mbeki, the South African president, for discussions on the 2010 World Cup, which is to be held in South Africa.
But the summit itself may be overshadowed by a row over Sudan's attempt to head the 53-member African Union.
The issue of chairman is the first item on the AU agenda and Chad has threatened to walk out of the meeting if Sudan is elected.
Last year, Khartoum agreed to hold off on its ambitions to chair the organisation for 12 months due to the outcry over the crisis in Darfur, where a 7,000-strong AU force was attempting to control the conflict.
But Lam Akol, Sudan's foreign minister, said Khartoum was now planning to take up the post.
He said: "The Sudanese presidency will be very good for the AU. The situation in Darfur has no relationship with that presidency."
The conflict in Darfur has claimed more than 200,000 lives and humanitarian groups say the situation in the region is worse than ever.
Desmond Tutu, the South African archbishop and Nobel prize-winner, said in a statement: "Africa cannot turn its back on the people of Darfur.
The government of Sudan continues to act with impunity and must now be subjected to tough and effective sanctions until the suffering ends."
He said: "Sudan's president, Mr Beshir, longs to be given the AU's presidency. The AU cannot allow itself to comfort the oppressor."
Human Rights Watch, a New York-based rights organisation, said in a letter to the AU that it should use its summit meeting "to reject Sudan's latest bid to become chair" on the grounds of its "record of crimes against humanity and war crimes in Darfur".
Sources at the summit said although Sudan was still the only official candidate, Ghana, Rwanda and Tanzania were possible compromises.
Another possibility would be for Congo, the current chair, to extend its tenure.