On Iraq's southeastern frontier with Iran, which Radio Tehran painted as the scene of pitched battles between the two nations, there is certainly no war, but there is ready evidence of Iraq's military confidence and power.

We spent a day traveling by jeep and helicopter, up and down some 100 kilometers of border where Iran has claimed Iraqi troops the night of Dec. 13 made a deep and bloody penetration. In fact, peace prevailed in the spring-like December of the oil-bearing desert. There were no signs of recent military operations or of preparations for future ones. except for a training exercise we happened on 60 kilometers from the border, we saw a very low Iraqi military profile.

But Iraqi officers here expressed confidence that Iran's once-mighty army, now in disarray, is no match for Iraq. The border war is imaginary (a desperate attempt by Iran's propagandists to restitch their country's fabric), but Iraq's new power is not. This leftist, authoritarian state, anti-Western but also anti-communist, has become the Persian Gulf's preeminent military power.

Tehran's reports of heavy fighting here, while denied by Baghdad as total fabrication, had a small kernel of reality confirmed to us by officers on the scene. A boatload of Iraqis came close to or actually crossed the border in marshy country near the city of Amareh. The Iraqis claim they were simple fishermen but acknowledge the Iranians thought them infiltrators sent in to stir up the overwhelming Arab population in Khuzestan (called Rabestan by Baghdad, to Tehran's anger) against Ayatollah Ruhollah Khomeini's regime.

Whether infiltrators or fishermen, they attracted rifle fire from Iranian Revolutionary Guards (contemptuously called "Khomeini guards" by Iraqi officers), which was answered by Iraqi border troops. The Iranians also fired two or three mortar rounds against the boat, which were not answered (apparently Amareh's "artillery duel" that became the talk of Baghdad's embassy row). The scorecard, according to Iraqi officers no hits, no damage, no casualties.

The story has the ring of truth, if only because the area shows no stigmata of military action or even motion. As we toured the cradle of civilization near the junction of the Tigris and Euphrates rivers and the claimed site of the Garden of Eden, there were few military sights competing with camels and flare-ups of natural gas in the oil fields. We saw no tanks, no artillery, no troop movements. Instead, there are sleepy Beau Geste-style border outposts, manned by overaged border guards (who nevertheless carry Soviet Kalishnikov automatic rifles). Typical is El Fakah, principal station in the Amareh area. Built by the British in 1920, its heaviest armament is 2.3-millimeter mortars. Although a similar Iranian outpost lies three kilometers away, nothing happened here during the supposed great battle of Dec. 13.

We would hardly have experienced the true Iraqi military machine had we not by chance encountered a training exercise at Alsha Arba air base, some 60 kilometers from the border. The runways were filled with Soviet-made MIGs of less than recent vintage but obviously superbly maintained, plus huge transport planes from which were pouring elite naval infantry.

"I bet you think we are going to invade Iran," one Iraqi officer told us, hastily explaining it was only a joint air-marine training exercise. When we returned to the air base at day's end, the planes and men were gone. We saw not a trace of them near the border, either on the ground or in the air.

Training exercise were also held that day (also far from the border) by the First Battalion of the 27th Brigade, principal army unit in Radio Tehran's "war zone." Its commander, Lt. Col. Abid al-Jaburi, claimed his men would handle the remnants of the shah's legions with ease. "Iran's army is on the shelf," he told us. "They have no role in their country."

Iraqis think there are no Iranian army units across the border here, only despised "Khomeini guards" and Iranian gendarmerie who regularly man border posts -- a further reason for confidence. "Let me tell you something," advised Col. Mahir al-Raschid, a general staff officer from Baghdad with the earmarks of an Iranian intelligence expert. "The men is those border posts still love their shahinshah. The gendarmerie always has. They will not fight for Khomeini."

Neither will Iran's erstwhile allies. In prolonged 1974 border fighting, Iraq pulled its punches out of fear of intervention by the shah's allies: Turkey, Pakistan, even the United States "Now," one colonel exalted to us, "Iran is alone; let them try something now, and we will take care of them."

Instead, officers of the First Battalion, 27th Brigade, seem itching for sufficeint provocation to bloody the "Khomeini guards." Their political leaders in Baghdad, while acknowledgeing Iran's probable desmemberment, do not see this as cause for sheer enjoyment, but as a possible obstacle to Iraq's leading role in the Persian Gulf.