Ethiopia's military leader, Lt. Col. Mengistu Haile Mariam, indicated here today that his government has no intention of invading Somalia despite what he called the "arrogant invasion" by the Somalis of the whole southeastern portion of this country.

In a speech marking the third anniversary of the military's overthrow of the late Emperor Haile Selassie, the Ethiopian chief of state said that Ethiopia had not violated Somali territory during th Current conflict and, he added, "never will," "but coming face to face with arrogant and aggressive (Somali) expansionists, we will struggle and crush them," he said.

Somalia has repeatedly expressed the fear that Ethiopia will shortly attempt to invade its territory to counter the takeover of the Ethiopian Ogaden region by Somali guerrillas aided by what now appears to be a growing direct involvement by regular Somali army.

The celebrations, here, including a five-hour parade before a crowd of more than 200,000 people, took place as both Ethiopia and Somalia reported that fierce fighting was still taking place "in and around" the Ethiopian town of Jigjiga.

The battle for the town, southeast of Harrar in Eastern Ethiopia, may well determine the entire future course of the seven-week-old war, which has suddenly taken on the dimensions of being the worst open conflict to have taken place anywhere in black Africa between two independent state.

If Ethiopia Joses Jigjiga, the road will be open to a direct attack by the combined Somali forces on the larger cities of Harrar and Dire Dawa, the latter being a key rail junction on the Addis Ababa-Djibouti railroad and the third-largest city in the country.

On the other hand, if Ethiopia succeeds in holding Jigjika, the likelihood is that the Somali plan to seize the other two strategic cities would be doomed to failure and the Ethiopians in a position to launch a strong counteroffensive to recapture the Ogaden region.

To the surprise of observers, Mengistu today gave no special praise to the Soviet Union, which has been pouring in arms ever since this country broke with the United States in April.

Also to the surprise of most observers, Mengistu did not single out the United States for special attack for aiding the country's enemies, as he has often done in the past.

Mengistu said that attempts by Somalia to annex the Ogaden and by Eritrean separatists in the north to create an independent state in Eritrea Province had turned Ethiopia into a "Fortress from one corner to the other."

He admitted to "temporary reverses" on three war fronts - in the Ogaden, in Eritrea and in southern Ethiopia, also against Somali insurgents - and said Ethiopia's revolution and national unity are in "a state of grave danger."

But he expressed confidence again and again that Ethiopia would emerge victorious on all fronts because, he said, it is fighting a "genuine people's war" and has the support of progressive countries around the world.

At this point, Somali guerrillas belonging to the Western Somalia Liberation Front have occupied practically all of the Ethiopian Ogaden and considerable additional land to the north and west as well, with only Jigjiga Harrar and Dire Dawa still in Ethiopian hands.

All indications are that the battle of Jigjiga which has been going on now for three weeks, has become a major encounter between the regular forces of the two opposing armies involving hundreds of tanks and armored cars.

The Ethiopians now claim to have knocked out 62 Somali tanks in and around Jigjiga since the beginning of this month and about 104 tanks and 28 Migs since the war began on a large scale July 23. Western diplomatic sources here believe that the Ethiopian figures are roughly accurate.

Sunday the Ethiopian media reported that the regular Somali army was engaged in its third major offensive to seize Jigjiga, which is a main Ethiopian army camp for the entire southeast containing a large tank training center.

It claimed that the offensive had met with the "heroic resistance" of regular Ethiopian forces as well as elements of the 100,000-man militia formed here last spring.

The Western Somalia Liberation Front claims to have already captured the town and says that its flag is flying over it now.

There has been no independent confirmation of this claim, however, and even the Somalis admitted Sunday that fighting was still going on inside Jigjiga.

Thus it remains unclear which side now really controls the town and it appears highly likely that fierce fighting is still under way there.