Iranian and Iraqi forces battled with gunboats, planes, rockets and artillery yesterday along the disputed Shatt-al-Arab estuary at the northern tip of the Persian Gulf, but both sides apparently stopped short of attacking vital oil installations on either side of the channel.

The two sides issued conflicting accounts of the fighting, with each claiming to have sunk or damaged several of the other's naval vessels on the 60-mile-long waterway between the two countries. Taken at face value, however, the two versions indicated that Iran was getting the worst of the fighting.

In Washington, Defense Secretary Harold Brown said yesterday that the fighting clearly has "gone beyond skirmishing" but is "not a major war." In an interview on the CBS Face the Nation program, he added: "I think it is very dangerous to both of those countries, it's very dangerous to all countries in the region, and it's potentially dangerous to the peace of the world."

Iranian military headquarters, quoted by Iran's official radio, said that both land and naval forces were involved in yesterday's clashes, which it said included artillery, missile and tank duels. The communique said an Iranian naval facility at the port of Khorramshahr was heavily damaged and that nearby Abadan Airport came under enemy bombardment.

Civil aviation officials said the airport would remain closed indefinitely.

The military communique also said Iranian forces sank an Iraqi naval vessel Saturday and forced four others aground. It said an Iraqi border post and an ammunition dump on the channel were destroyed.

The statement added that one Iranian naval vessel was sunk and a freighter damaged by Iraqi fire. It said casualties would be announced later.

In Baghdad, an Iraqi military spokesman said an Iranian Phantom fighter-bomber was shot down and three Iranian patrol boats sunk in the Karun River yesterday.

Earlier, the official Iraqi News Agency claimed that Iraqi forces destroyed five Iranian gunboats and the Iranian naval base at Khosrowabad, 20 miles south of Iran's giant Abadan oil refinery. Quoting a military spokesman, the agency said the Iranian vessels were sunk after two Iranian gunboats intercepted a British cargo vessel on the Shatt-al-Arab The spokesman said several Iranian crewmen were killed.

Military spokesmen in Tehran refused to comment on the Iraqi reports.

The Iraqi News Agency, said that "Arab youths of Arabistan" had rocketed Abadan Airport and the port of Khorramshahr, killing and wounding "several" persons. Arabistan is the Arabic name for Iran's Khuzestan Province, where the ethnic Arab majority has been struggling sporadically for autonomy since shortly after Iran's revolution.

A senior official of the National Iranian Oil Co. said he believed Iranian forces had consciously not fired at oil installations in the Iraqi port city of Basra "because they can do the same to us."

The official said there was heavy fighting yesterday morning in areas close to Iran's largest oil refinery at Abadan and that Iraqi shelling started several fires. But the refinery itself was not hit, and the fires nearby were put out quickly, he said.

The fighting was the worst between the traditional rivals since hostilities flared in the spring.

Fighting along the 720-mile border separating the two countries spread to the Shatt-al-Arab after Iraqi President Saddam Hussein announced on Wednesday that he was abrogating a 1975 border agreement with Iran and was taking full control of the estuary, shared by the neighbors under the five-year-old pact.

Iraq claims it is now the sole legitimate authority in the waterway and has ordered all vessels using it to fly the Iraqi flag and pay Iraqi navigation fees.

Iraq has launched a diplomatic offensive to advise foreign nations of its actions. Baghdad says it is seeking the return of "usurped" territory from Iran, while Tehran accuses Iraq of making vague claims under the pact to seize Iranian territory and of trying to wreck the Iranian revolution.

The Iraqi News Agency said Tareq Aziz, a close adviser to President Hussein, flew to Moscow yesterday for an official visit. Iran's state radio, meanwhile, reported that Soviet ships carrying military vehicles and equipment arrived at the Iraqi port of Basra on Thursday.

Tehran's embattled revolutionary government, with some of its troops tied down fighting rebel tribesmen in Kurdistan, Saturday ordered several thousand reservists called up for military duty in what was seen as a largely symbolic gesture.

The Shatt-al-Arab waterway is critical to Iran. Iranian crude oil is mainly shipped from Kharg Island in the Persian Gulf, but products from the Abadan refinery are exported from a terminal on the channel, which is also used by ships calling at the major Iranian port of Khorramshahr.

However, the fighting between Iran and Iraq threatens no immediate worldwide shortage of oil unless it spreads elsewhere in the Persian Gulf, oil industry executives said in London yesterday.

They said noncommunist world stocks are glutted with enough oil to meet 100 days' normal demand because of a recession-induced fall in consumption.

These would act as a cushion if Iraqi and Iranian exports are hit, and even if other members of the Organization of Petroleum Exporting Countries then persist in making 10 percent production cuts, agreed on at a meeting in Vienna last week, the industry sources said.

But they added that, while Iranian exports are marginal, a prolonged interruption of the bulk of Iraqi exports would turn today's glutted market into a tight one this winter. Iraq currently produces about 3.5 million barrels a day compared to Iran's estimated 1.5 million barrels a day.