Iran's armed forces today claimed fresh advances in their now week-old invasion of southeastern Iraq despite a three-pronged Iraqi counteroffensive to dislodge them from their Faw Peninsula bridgehead.

Although sources with access to satellite photographs reported no change on the ground in three successive days, Iranian spokesmen said their forces seized nearly 20 more square miles in fierce overnight fighting against Iraqi reinforcements.

The spokesmen claimed that 2,700 Iraqis were killed or wounded in a "lightning" Iranian attack at an unspecified location between Faw on the Shatt al Arab estuary and the Umm Qasr naval base 35 miles to the west.

Tehran radio reported more reinforcements moving into a 30-mile front inside the Faw bridgehead, which so far has been the most successful Iranian operation inside Iraq since the Persian Gulf war began in September 1980.

In Baghdad, foreign diplomats were quoted as predicting a major Iranian offensive in the marshes north of the southern port city of Basra on the basis of reported troop concentrations around Susangerd and other border towns.

The Iraqis, who today for the first time admitted losing Faw, provided few details in repeating their insistence that their troops are "nearing the accomplishment of the final crushing of the Iranians who crossed the Shatt al Arab."

But Iranian troops seemed so unconcerned about Iraq's counteroffensive that they took Tehran-based foreign correspondents to the Faw bridgehead today.

Reporters were shown positions a mile north of the unused Iraqi oil port at the head of the gulf and four miles to the west. Reuter reported from Tehran that the visiting reporters believed the front was far enough away to keep them out of range of Iraqi heavy artillery.

Tehran radio said Iran's armed forces controlled 320 square miles around Faw, and had killed or wounded 12,700 Iraqis last week.

Iranian television said 2,105 enemy soldiers had been captured this week and 24 aircraft had been shot down.

The foreign ministers of Iraq's two most important Arab allies, Saudi Arabia and Kuwait, flew today to Syria, which with Libya and, to a lesser extent, Algeria is among Iran's only Arab friends.

Unconfirmed reports suggested that an Iranian representative would be present in Damascus during the talks, which are expected to focus on a U.N. Security Council meeting on the gulf war, scheduled to start in New York on Tuesday.