Iranian and Iraqi forces were engaged yesterday in what American officials called "furious battling" about 12 miles inside southeastern Iraq, a day after the leading edge of an 80,000-man invasion force moved across the border from Iran.

Officials here indicated that it was too early to tell from intelligence estimates available yesterday whether either side has gained the upper hand in what could be a showdown battle between Persian Gulf neighbors who have been at war with each other for almost two years.

They were engaged in infantry, tank and artillery battles yesterday, according to government sources here. The initial Iranian objective appeared to be to try to wipe out all Iraqi resistance in the roughly 15 miles between the Iranian border and the strategic Shatt al Arab waterway leading into the Persian Gulf.

Although military communiques on the fighting are being issued by both sides, their claims are often conflicting and cannot be confirmed independently because western journalists have not been allowed to travel to the front.

The invasion, which the Iranians say began Tuesday night (about 2 p.m. EDT), has created grave concern here and in Persian Gulf states such as Saudi Arabia and Kuwait that an Iranian victory would topple the Iraqi regime and threaten several governments in the region with another Islamic fundamentalist revolution.

Emerging from a special briefing at the White House yesterday, Senate Majority Leader Howard H. Baker Jr. (R-Tenn) told reporters that, with roughly five Iranian divisions pitted gainst seven Iraqi divisions, there is "a very real danger the war will spread. . . . The indications are there is a real danger of a major conflict."

A statement issued later by deputy White House press secretary Larry Speakes said the United States would continue its policy of neutrality toward both nations in the conflict. But the statement expressed deep concern over the developments and said Washington was prepared to consult with "friendly states" in the region "on appropriate steps to support their security."

Administration officials said later that those consultations already had begun with Saudi Arabia, Egypt, Jordan and Israel, among others.

Speakes did not say what those "appropriate steps" might be. Other officials pointed out that in October, 1980, when Saudi Arabia felt threatened by Iran at the start of the Iran-Iraq war, the United States dispatched four airborne warning and control system (AWACS) planes to help patrol Saudi airspace and warn of any potential Iranian air attacks. Saudi Arabia has backed Iraq financially in the war.

Those four planes, which are manned by American crews and can electronically "see" things hundreds of miles away, are still in Saudi Arabia. Government sources hinted yesterday that the radar planes are an important source of current intelligence about what is going on at the war front.

It could not be determined yesterday whether the United States is considering taking new steps in the current crisis similar to the earlier dispatch of AWACS planes. Some officials speculated that U.S. Navy ships now in the Indian Ocean might be moved closer to the Persian Gulf.

Beyond clearing out the border region and approaches to the Shatt al Arab waterway, the next main military objective of the Iranian thrust appears to be the Iraqi oil port of Basra, which lies just across the waterway in the extreme southeastern corner of the country. Basra is Iraq's second largest city and its main outlet to the Persian Gulf.

Tehran radio reported late yesterday that Iranian forces had advanced 15 miles into Iraq and were now within nine miles of Basra. American officials said at the time that they could not confirm that the Iranians had advanced that far.

The Iranian forces, equipped with river-crossing equipment believed to include pontoon bridges, would have to cross the waterway to reach Basra or be in position to threaten it. The Iranians have never done this kind of maneuver under combat conditions, according to analysts here.

Aside from reiterating that the United States "has remained from the beginning, and will remain, neutral in the war," the formal White House statement said the United States "supports the independence and territorial integrity of both Iran and Iraq," opposes seizure of territory by force and "urges an immediate end to hostilities, and a negotiated settlement."

U.S. support "for the security of friendly states in the region which might feel threatened by the conflict is well known, and the United States is prepared to consult with these states on appropriate steps to support their security," the statement said.

The United States has no formal diplomatic relations with and little or no influence over either country, although some American diplomats are in Iraq. That situation makes the crisis especially frustrating for Washington because the outcome could be so potentially serious for U.S., allied and moderate Arab interests in the oil-rich gulf region.

Instability in the region also could produce new efforts at Soviet penetration and result in an East-West clash.

There also have been numerous unsuccessful attempts by third parties--the United Nations, Islamic groups, nonaligned groups, Turkey, Pakistan and Algeria--to find a peaceful settlement to the war.

"We are limited in what we can do directly," Secretary of State-designate George P. Shultz told questioners during confirmation hearings yesterday before the Senate Foreign Relations Committee. "We should work with our friends in the region . . . and also with the Japanese and Europeans who also have a great stake" in the gulf region, he said.

Baker referred to "the Saudis, the Jordanians and others" who are "greatly concerned by this conflict and what it portends."

Baker said it portends an Iranian attempt to set off a Shiite fundamentalist revolution that initially would take power in Iraq, a country with a Shiite majority although it is ruled by Sunni Moslems, and then spread to other countries with large Shiite populations.

Senate Armed Services Committee Chairman John G. Tower (R-Tex.) also warned of the threat that a Shiite government takeover in Iraq might precipitate similar takeovers in other countries. Tower said the United States should do its best to strengthen friendly regimes in the area but should not get involved directly.

House Foreign Affairs Committee Chairman Clement J. Zablocki (D-Wis.) said he would support arming Iraqi forces indirectly by transferring U.S. weapons supplied to other Persian Gulf states. No one in the administration has told him such an idea is under consideration, he said.