Iraq said today its forces had completed the capture of the embattled Iranian port city of Khorramshahr, opening the way to throwing its full weight into the seige of the oil center of Abadan.

It was the fourth in as many weeks that the Iraqis had claimed Khorramshahr had fallen. Each of the previous claims was denied by the Iranians and followed by continued fierce fighting that has left the city in a shambles.

Again today, Iran claimed that bitter fighting continued inside the city, but in contrast to the earlier times, convincing details were missing in the denial. For instance, more than four weeks ago when Iraq was embarrassed and forced to withdraw its claim that the city had fallen, the Reuter bureau in Tehran was able to call residents of the city who affirmed that Iran was still in charge.

There was none of that today.

Instead, an announcement on Iraqi television said troops had stormed across a vital bridge early this morning, taking it and opening the way for Iraqi forces to stream into the city, routing the final Iranian defenders.

The capture of Khorramshahr would be a major victory for the Iraqis, since the stubborn defense put up by the Iranians has given it great psychological importance in a war that has gone on longer than initially expected.

The Iraqi announcement today also made clear that the fall of the city had come at a heavy price.

"The Iranians were defeated in Mohammerah [the Arab name for Khorramshahr] after much bloodshed by our heroes," the television announcement said, indicating that there had been heavy Iraqi losses.

The Iraqi forces have moved with great caution throughout their drive into Iran's Khuzestan Province, softening up Iranian positions with day after day of artillery and tank shelling before committing troops to battle, apparently in an effort to avoid heavy casualties that could prove to be a political liability at home.

The battle for Khorramshahr proved to be impossible to finish without heavy house-to-house fighting, however, because of the determined resistance put up by the Iranian military and Revolutionary Guards.

The city had more than 150,000 inhabitents before the battle began and was Iran's largest cargo port. Most of the population fled after the war started, and parts of the city had been left in rubble by constant artillery and mortar shelling.

Special prayers of thanksgiving for the fall of Khorramshahr were held in most Iraqi mosques tonight on the traditional Moslem sabbath.The Iraqi News Agency said word of the victory was flashed to President Saddam Hussein by Gen. Adnan Khairallah, the defense minister, who was reported to be on the fighting front.

With the capture of Khorramshahr, Iraq said its forces are now able to completely besiege the oil-refinery city of Abadan. Abadan is an island, with the Karun River forming one side of it and the Shattal-Abab the other. The bridge over the Karun gives Iraqi troops complete access to the city, which is 10 miles from Khorramshahr. Previously, most of the action in Abadan was confined to long-range artillery shelling from the Iraqi side of the Shatt and some skirmishes on the city's outskirts.

Tehran radio said today that Iraqi forces were firing on residential areas of Abadan from two sides and indicated that the intensity of the attack was building.

Iraq also claiming that it was stagging artillery attacks on Ahwaz, the capital of Khuzestan Province, which contains most of the country's oil.

The Iraqi News Agency also announced tonight that Baghdad had agreed as a humanitarian gesture to allow the more than 100 ships trapped in the Shatt to leave if they fly an International Red Cross flag.

The offer, however, means little, since Iran has been firing on ships trying to leave the waterway or send sailors ashore, and Tehran still controls the entrance to the channel.

Previously Iraq had said all ships had to fly its flag.

Baghdad said it decided to allow ships out at the request of U.N. Secretary General Kurt Waldheim.

Iran's official Pars News Agency, in addition to claiming its continues to hold Khorramshahr, said Iraqi forces had been pushed back from Ahwaz and from the towns of Bostan and Susangerd in the central battle sector. It had Iranian helicopter-borne troops had captured 19 Iraqi tanks in fighting in the northern sector.