But the German government has ruled out compensation for victims’ descendants.
A group of Herero has filed a case against Germany in the United States demanding $4bn in compensation.
“We Germans accept our historic and moral responsibility,” Ms Wieczorek-Zeul, Germany’s Development Aid Minister, told a crowd of some 1,000 at the ceremony in Okokarara.
“Germany has learnt the bitter lessons of the past.”
But after the minister’s speech, the crowd repeated calls for an apology.
“Everything I said in my speech was an apology for crimes committed under German colonial rule,” she replied.
The Herero rebelled in 1904 against German soldiers and settlers who were colonising south-west Africa.
Driven into desert
In response, the German military commander, General Lothar von Trotha, ordered the Herero people to leave Namibia or be killed.
Germany argues that international laws to protect civilians were not in force at the time of the conflict.
Herero chief Kuaima Riruako said the apology was appreciated but added: “We still have the right to take the German government to court.”
However, correspondents say the lawsuit filed in the US three years ago against the German government and two German companies is seen as having a limited chance of success.