Iran's occupation of Iraq's Faw Peninsula, now well into its second week, has embarrassed Baghdad, which was initially caught off guard and still has been unable to oust the invaders from the mouth of the strategic Shatt al Arab waterway.

Sources with access to satellite photographs confirmed Tehran's repeated claims that Faw was firmly in Iranian hands despite a major, three-pronged Iraqi counteroffensive that apparently has been stymied in its fifth day.

Even Iraqi commanders, who for days insisted Faw was still under their control, now concede that the fight to win back the peninsula at the head of the Persian Gulf is progressing by "inches" -- as if to suggest that more hard slogging lies ahead.

Military analysts blame principally the strangely inactive Iraqi Air Force for the virtual stalemate that has allowed the invaders to dig in at the Faw Peninsula and in its immediate environs.

The Iranians, resupplied under cover of darkness by pontoon bridges and small boats over the swiftly flowing Shatt al Arab, occupy strong defensive positions in the marshy tidal salt flats that cover much of the peninsula.

Despite boasts of cutting off southern Iraq from its Kuwaiti, Saudi Arabian and other Arab allies on the gulf's west coast, the Iranians appear content to sit and wait for the Iraqis to attack their expanded bridgehead.

Wary of committing strategic reserves to Faw when a major Iranian offensive is expected momentarily at more vulnerable sectors to the north, Iraqi President Saddam Hussein twice has visited the front and, in the view of observers here, apparently has decided to make haste slowly.

Although Faw's usefulness as an oil-exporting port was ended by Iranian shelling in the war's first week in 1980, Iraq can ill afford to let the Iranians stay there without risking potentially destabilizing psychological and political damage at home and among its Arab neighbors, according to diplomats.

But a full-fledged drive to retake the bridgehead, which Tehran claims covers 322 square miles, could prove costly in casualties.

In addition, because of the marshy terrain around the Iranian pocket, the mobile, highly motivated -- although lightly armed -- invaders appear well placed to use nighttime commando tactics to extract a high toll on Iraq's counteroffensive.

With Baghdad's Air Force seemingly unable or unwilling to provide sustained, effective low-altitude ground support, the Iraqis, who have four times as many warplanes as the Iranians, appear at a tactical disadvantage.

Their Soviet training has made them reliant on massive use of air power, heavy artillery and armor -- which, unlike Iran, they have in profusion -- to saturate enemy positions before committing infantry.

But this tactic -- while sensible for Iraq, whose population is less than a third that of Iran and whose troops are less fervid than Iranian troops -- appears ill adapted to the Faw sector.

Except for three exposed roads, the terrain is often covered at high tide and is too soggy for tanks, especially so soon after the latest rainy season.

Satellite photographs are said to show that the Iranians have brought no heavy weapons or armor with them.

Even discounting rival claims of massive casualties in the Faw fighting, Tehran would appear to have succeeded in its favorite tactic of bleeding its enemy.

In the final analysis, according to observers, Iraq may be proved right in asserting that the invaders are trapped on the peninsula. But, the observers say, Tehran, which has already accepted massive casualties in the 5 1/2-year-old war, may be willing to sacrifice its Faw force to hasten the end of Saddam Hussein.

So far, there has been no visible result from the recent flurry of activity involving the pro-Baghdad foreign ministers of Saudi Arabia and Kuwait during a visit to Syria.

Whatever misgivings Syrian President Hafez Assad may have about the Iranian occupation of Arab land, so strong is his hatred of the Iraqi regime that he is thought likely to have dismissed the emissaries' latest proposals.