Ethiopia's Marxist ruler Col. Mengistu Haile Mariam yesterday ordered national mobilization against "open invasion" by Somalia.

Speaking on Addis Ababa radio, he conceded the loss of three towns in the disputed Ogaden Desert region of southeastern Ethiopia and said fierce fighting was going on against Somali regular forces around the major centers of Harrar and Dire Dana in the month-old war in the Horn of Africa.

A later Addis Ababa broadcast announced a reshuffling of top military commanders to meet "invading enemies."

Somalia hinted it may break relations with the Soviet Union because of the Kremlin's support for Ethiopia in the desert war. Diplomats in Mogadishu reported heavy fighting near Jigjiga, in addition to Dire Dawa and Harrar, and said both sides appeared to be gearing up for a major showdown battle.

Mengistu admitted in his 30-minute broadcast that fighting also was raging in the Red Sea province of Eritrea, where his army is contending with secessionist guerrillas.

Mengistu called for "national mobilization," adding that directions and plans to mobilize will be issued later.

Mengistu said he wanted to remind President Siad Barre of Somalia of the fate of Italian dictator Benito Mussolini, whose army invaded Ethiopia in 1935 and was driven out during World War II.

Somalia has denied using its regular forces in the battle to control the Ogaden Desert, but it openly supports the secessionist Somali guerrillas.

Mengistu said yesterday that Somali regular soldiers have been killed near Harror and Dire Dawa.

He said Somalia has taken advantage of the onslaught further north in Eritrea by the different secessionist movements there and that "reactionary Arab counties" have stepped up help to the Eritrean secessionists.

Mengistu said Somalia's rulers and the Eritrean secessionists "should be taught an unforgettable lesson now."

"Everything to the battlefront," he said. "Revolutionary motherland or death."

Ethiopia's regular forces number about 60,000. These have been bolstered by a people's militia, the so-called Peasant Army, and the Soviet arms.