ASMARA (Reuters) - Washington`s senior diplomat for Africa shuttled between Eritrea and Ethiopia on Monday to mediate in a violent border row that shows no signs of abating. Eritrean officials said Susan Rice - the under-secretary of state for Africa - arrived in Asmara on Saturday night, travelled to Addis Ababa on Sunday and then returned to Eritrea early on Monday. Rice met Ethiopian Prime Minister Meles Zenawi in Addis Ababa and Eritrean President Isayas Afewerki and visiting Djibouti President Hassan Gouled Aptidon in Asmara, the officials told Reuters. They gave no details of the talks and U.S. officials were not immediately available to comment. But in the Ethiopian capital on Monday, state radio quoted Foreign Minister Seyoum Mesfin as saying his country would reject international mediation efforts until Eritrea unconditionally withdrew its troops. Seyoum would make a full statement later in the day after meeting with foreign diplomats, the radio said. Eritrean officials said Rice`s involvement in the row between the Horn of Africa neighbours illustrates Washington`s desire to see a quick resolution to the conflict between two of its staunchest African allies. Regional African leaders have also become involved in efforts to mediate with Rwandan and Ugandan leaders holding talks with Afewerki over the weekend. The conflict was cited on Friday by the Democratic Republic of the Congo as the reason for cancelling a weekend summit of African leaders which was supposed to have marked the first anniversary of President Laurent Kabila`s overthrow of former Zaire dictator Mobutu Sese Seko. Ethiopia and Eritrea have disagreed peacefully over their lengthy border ever since 1993, when Eritrea gained independence from Ethiopia, but the spat turned violent earlier this month with both sides accusing the other of invading. Eritrea independence came after a gruelling 30-year war of liberation and Eritreans played a key role in the alliance that ousted Ethiopia`s Marxist dictator Mengistu Haile Mariam in May 1991. On Sunday, thousands of Eritrean troops took up positions in the disputed territory, a 400 sq km triangle of land on the west of their border, witnesses said. Reporters on a tour of the area saw ample evidence of Eritrean military deployment towards the border town of Badme, where Eritrean and Ethiopian troops first clashed on May 6. Residents in Badme told Reuters they had lived in the area for decades and considered themselves to be Eritrean. Eritrea has admitted its army engaged Ethiopian forces but insists it has merely retaken land which its neighbour grabbed six months earlier. Ethiopia has threatened to make a "firm response" unless the Eritrean forces unconditionally withdraw from the territory. Unconfirmed reports circulating in Asmara on Monday said Eritrea had sent hundreds of troops to reinforce other areas of the border.