Iraq admitted today that Iran had launched an offensive in the mountains north of here in an apparent effort to increase pressure on the Iraqi Army after Iran's capture almost three weeks ago of the Persian Gulf oil terminal port of Faw.

The Iraqi admission of the attack in the Kurdistan mountains, coming two full days after it was announced in Tehran, appeared to confirm the opinion of foreign military observers here that Iraq was being put very much on the defensive in its 5 1/2-year-old war with more populous Iran.

The Iraqi News Agency confirmed this afternoon what Iran had been reporting for two days -- that its forces had pushed into Kurdistan, northeast of Baghdad, in a new effort to break across Iraq's increasingly vulnerable borders.

The brief Iraqi statement said that the Iranians had pushed 20 miles into Iraqi territory to the immediate northeast of the provincial Kurdistan capital of Sulaymaniyah, about 90 miles from the Iraqi oilfield center of Kirkuk.

The Iraqi statement said that the Iranian assault by a brigade estimated at 3,000 men, had been contained and that the attackers had suffered severe casualties.

The Iranian news agency IRNA announced two days ago that its forces had captured about 25 Iraqi villages in the rugged mountainous area to the east of Sulaymaniyah, an area in which they had had a military success in 1983 before being pushed back by an Iraqi counterattack through the area of steep mountains and narrow valleys that prevent the use of advanced military equipment such as tank columns. Iran said today that it had seized about 100 square miles of Iraqi territory in the region.

Western military sources in Baghdad confirmed the Iranian incursion into Kurdistan but dismissed its overall importance because the area's ruggedness does not lend itself to major military movements.

"There is no doubt the attacks have taken place," said one western military observer in the Iraqi capital who declined to be identified further. "But the area is so rugged, so isolated, that the attack does not seem to seriously threaten Iraq, or its oil fields in Kirkuk." The official said, however, the attack could be seen as an effort to challenge the Iraqi Army and its reserves, which already have been pressed hard by the much more serious Iranian offensive in the Faw Peninsula on the Persian Gulf immediately south of Basra, Iraq's second city.

The Feb. 9 attack on Faw has presented the Iraqi Army with one of its greatest challenges in the war that began in September 1980 when Iraqi forces invaded Iran's Khuzistan Province east of Basra.

For the first time since that war began, Iranian forces have succeeded in capturing an Iraqi city -- albeit one that virtually had been abandoned by its population the first days of the war -- and blocking Iraq's outlet to the Persian Gulf through the Shatt al Arab waterway that divides the two countries.

Iraq responded to the surprise Iranian amphibious and helicopter attack by claiming that the Iranians would be repulsed swiftly from the southern peninsula near the Kuwait border. In the last few days Iraqi generals in command of the counterattack against the Iranians have admitted that their efforts were meeting strong resistance and that their predictions of early victory may have been premature, given the difficult terrain of salt flats and flooded plains that they must fight across to reach the Iranians in Faw.

Western military observers monitoring the bitter war between the two Persian Gulf nations said today that the statements to journalists by Iraqi generals fighting in Faw seemed to be admissions that the campaign to push the Iranians out of the town might take a long time, given past Iraqi unwillingness to commit infantry in the sort of hand-to-hand combat that would be necessary to dislodge the enemy.

The Kurdistan attack admitted today was seen more as a well conceived Iranian harassing effort to disrupt the Iraqi military efforts to retake Faw than as a major offensive aimed at the oil fields of Kirkuk, one of the most highly defended areas in Iraq.