Intense air and ground battles broke out this morning as Iran launched a new offensive in the rugged and isolated mountains of northeastern Iraq.

Iraqi military spokesmen acknowledged that Iran, apparently with the help of Kurdish rebels, had been able to penetrate the Iraqi border. But they said Iraq had been able to contain the attack. The Iraqi spokesmen reported that heavy fighting continued tonight.

According to reports from Tehran, the Iranian objective was merely to cut an Iraqi supply route to dissidents in Iran and to seize mountaintop artillery positions that have been used to shell Iranian towns.

But there was speculation here that the new thrust might be much more ambitious and aimed at taking advantage of Kurdish unrest in northern Iraq to advance to vital oil installations from the northeastern border, reportedly defended only lightly by the Iraqis.

The fierce fighting appears to be around the area of Haj Omran, a border town in the Kurdistan area of northeastern Iraq.

In Baghdad, military spokesmen claimed that Iraqi troops had killed more than 600 Iranian soldiers. They said their forces had shot down an Iranian jet in a dogfight in the course of 159 air missions launched in support of the ground forces. They also claimed to have inflicted heavy damage on Iranian military equipment, prompting the surrender of large numbers of Iranian soldiers.

Iran said its forces had captured the Iraqi barracks at Haj Omran, used as a supply base for Kurdish rebels in Iran, Reuter reported from Tehran. The Iranian news agency IRNA said this was Iran's "most important objective." The agency also reported the capture of 8,500-foot King Mountain overlooking Haj Omran.

Tehran radio quoted a military communique as saying more than 3,600 Iraqi troops had been killed, wounded or captured, Reuter said.

Iraq has accused Iran of abandoning its military aims to wage a war of economic attrition. Both of the two once potent oil powers have endured severe economic losses in their nearly three years of war.

Earlier this week, Iraqi Foreign Minister Tariq Aziz said his country planned major new attacks on Iranian oil installations in an effort to severely damage the Iranian economy. But he acknowledged then that the Iranians apparently were preparing for a new attack.

The new fighting put a damper on the annual celebration commemorating the overthrow of the late king Faisal and appeared to deepen despair over the costly war. Iraqi television showed a grim-faced President Saddam Hussein visiting the northern front, where he studied maps and met with commanders. The footage showed Saddam Hussein viewing the harsh hills where the fighting is going on.

The mood in Tehran reportedly was joyous. According to dispatches from there, the government-run radio canceled scheduled programs and substituted accounts of the battle interspersed with music.

Both Iran and Iraq say the Kurds are the key players.

Referring to them, the Iraqis said the invading Iranian troops had been supported by "saboteur agents."

The Kurds inhabit an area that extends from southeastern Turkey through northeastern Iraq to northwestern Iran.

Even as Iran and Iraq have fought one another, both have cooperated with Turkey to crush the Kurdish struggle for independence

In June, Iraq permitted thousands of Turkish soldiers to cross its northern border in what appeared to be an effort to shore up the Saddam Hussein government in the midst of a Kurdish uprising.

Aziz, the Iraqi foreign minister, was asked this week whether the Turkish operation indicated that Iraq had lost control over Kurdish areas in the northern part of the country. He replied that the "destructive element of sabotage" threatened both Turkey and Iraq, and that it was for this reason that Iraq had allowed the Turks into the area. He said that the Turks had agreed not to penetrate more than about 2 1/2 miles deep on a front no more than about seven miles wide and not to continue the operation for more than 72 hours.

Tonight the radio offered an increased amount of Kurdish music in an apparent effort to rally support in the embattled northern areas.