The Islamic Courts Union, which controls much of southern Somalia, has refused to meet the interim government for peace talks unless Ethiopian troops leave the country.
Ibrahim Hassan Adow, the Islamic courts top foreign affairs official, said the movement could not accept the presence of Ethiopian soldiers in Somalia or Kenyan mediation during the peace process.
"We demand the exclusion of Kenya," he told Mogadishu-based HornAfrik Radio. "The government of Kenya is not neutral in the Somali conflict and its presence will not be accepted by the Islamic courts."
Although an 18-strong Islamic delegation flew to Sudan on Sunday, Adow said they would not engage with the largely powerless interim administration until Ethiopian troops leave.
"The transitional federal government is an institution serving the interests of Ethiopia, therefore we are demanding the immediate withdrawal of troops from Addis Ababa," Adow added.
The third round of talks, scheduled to start on Monday, was supposed to focus on power sharing between the two rivals amid fears a war could engulf the region.
The transitional government has said it will attend, but has repeatedly accused the Islamic courts of trying to undermine the talks.
"The Islamists are trying to undermine the peace efforts," Salad Ali Jelle, the transitional government's deputy defence minister, said. "They don't want peace."
Some countries are concerned that Ethiopia and Eritrea, who fought a bloody 1998-2000 war over their border, have turned Somalia into a proxy battleground for their dispute.
A confidential UN briefing note obtained by the Associated Press news agency says diplomatic sources estimate that "between 6,000-8,000 Ethiopians" are supporting the government and that "2,000 fully equipped Eritrean troops are now inside Somalia" backing the Islamic courts.
Ethiopia has repeatedly denied reports it has soldiers in Somalia but has acknowledged sending military advisers to help protect the largely powerless transitional government.
"The transitional federal government is an institution serving the interests of Ethiopia, therefore we are demanding the immediate withdrawal of troops from Addis Ababa"
Ibrahim Hassan Adow, foreign affairs official for the Islamic Courts Union
Eritrea angrily denied reports that it had 2,000 troops in Somalia.
"This campaign and continuous lie is a fabrication of the US administration," the Eritrean foreign ministry said, accusing Washington of supporting alleged Ethiopian plans to invade Somalia.
"The truth behind this campaign is to cover up the US government's plans and war it is carrying out in Somalia and the Horn of Africa in general through its agent, the [Ethiopian] regime," it said in a statement posted to its website.
Kenya was appointed co-chair of the Khartoum talks earlier this month after the transitional government accused the Arab League, which had been the sole mediator in two earlier rounds, of bias toward the Islamic group.
But the Islamic courts accuse Kenya of bias as it supports the government's call for regional peacekeepers.
Kenya currently holds the presidency of the Inter-Governmental Authority on Development (IGAD), a group of seven east African nations, which brokered the formation of the government in 2004 and now plans to send peacekeepers.
Somalia has been without a functioning central administration since 1991 and the current transitional government is unable to assert control over much of the country.