Muhammad Abdi Yusuf, the deputy speaker of the Transitional National Assembly and acting leader of the TNG delegation to the talks told IRIN that Ethiopian forces had "occupied parts of Somalia over the past few days".
In a separate press statement issued on Tuesday, the TNG accused Ethiopia of sending military forces "with heavy armour, including tanks", into parts of Somalia.
In a recent interview with the BBC, Ethiopian Prime Minister Meles Zenawi admitted his country had occasionally sent troops into Somalia to attack members of the Islamist al-Ittihad group.
"We hope that the international community appreciates our position that mediation by the Ethiopian government between the TNG and the opposition is neither reasonable nor fruitful," the TNG statement said.
"So long as Ethiopia is part of the mediation group, the TNG will not participate," Muhammad added. He said the TNG had no confidence in Ethiopia and "sees no point in continuing to be part of a conference managed by Ethiopia".
Ethiopia, along with Djibouti and the conference's host Kenya, is part of the regional Inter-Governmental Authority on Development (IGAD) technical committee which is steering the talks.
Also threatening to pull out of the talks is the so-called G8 group of factions, which has also accused Ethiopia of "invading" Somalia.
Mogadishu-based faction leader and G-8 spokesman Mawlid Ma'ane told the press on Monday that his group was considering withdrawing because of Ethiopia's "aggression".
A regional analyst involved in the talks told IRIN that if the two groups were to go ahead with their walkout threat, "the talks would probably collapse". He acknowledged that the talks were "in serious trouble and will need a great deal of effort to salvage".
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