The faction was trying to seize the border town of Dolo.
Hussein Ali, a spokesman for the Somali Muslim militant group Al-Itihad Al-Islam, said in Nairobi that the fighting Monday killed five Ethiopian soldiers and eight militants.
In August, Ethiopian troops seized Dolo, previously held by the Muslim group. The town is divided by a river into Somali and Ethiopian halves; a bridge linking the two sides was said to have been destroyed in the latest fighting.
U.N. officials, who spoke on condition of anonymity, said it appeared that Al-Itihad, in control of much of Western Somalia, had attacked the rival Ethiopia-backed Somali National Front in Dolo when Ethiopians fired backed in support of the front, one of Somalia's many factions.
Tensions between Al-Itihad -- or ''Islamic Unity'' -- and Ethiopia have been high since August, when Ethiopia said it killed more than 200 people in a swift cross-border attack on suspected Al-Itihad bases.
Al-Itihad, led by militant Muslim leader Ahmed Bille Hassan, has fought since 1992 to join the Ogaden region of eastern Ethiopia with Somalia into an Islamic state. The region is largely inhabited by ethnic Somalis.
There were no further reports of fighting in the area, nor comments from Ethiopian officials.
The SNF is made up of supporters of late dictator Mohamed Siad Barre, who was ousted in 1991 when Somalia disintegrated into fiefdom of warring factions.
Al-Itihad is said to be receiving arms and money from Sudan.
=A9 Copyright 1996 The Associated Press