Faced with mounting demonstrations that reached a new peak today, the South Korean government held out the promise of political concessions that it hopes will end the turmoil.

Prime Minister Shin Hyon Hwack, in a televised appeal for order, said the government is willing to consider quickening the pace of constitutional reform "to the maximum degree to respond to aspirations of the people."

The offer to satisfy a key demand of demonstrating students was vaguely worded, but other sources said the government is preparing a package of political concessions to be announced later.

With about 60,000 students packing the downtown streets for a third day of demonstrations, Shin coupled the offer with a warning that the government would not put up indefinitely with what he called an effort to "destroy law and order." He said the demonstrations were "paralyzing the social order" and appealed to students and their parents to restore stability.

The students marched, singing and chanting, in long columns through the downtown area, defying martial law in the biggest turnout since off-campus demonstrations began Tuesday night.

Repeated clashes with riot police were reported from late afternoon until about 10 p.m. and for the second consecutive day, downtown Seoul was filled with tear-gas fumes.

One police officer was reported killed, and at least 13 others were injured. There were no reports of student injuries or arrests. Police did not report any mass arrests, and military forces intervened only to guard key government buildings.

The government had been virtually immobilized in attempt to respond to the growing unrest except for a series of statements alternately appealing for peace and threatening punishment to the students.

Many observers believe its indecisiveness stems from a tug of war between some civilian officials and military officials who wield considerable influence within the interim government that took office after the assassination last fall of president Park Chung Hee.

But statements issued to the cencored press and confirmed by other sources hinted today that several concessions tentatively have been agreed on. They include:

An agreement to set a specific date, probably in September, for submitting constitutional reforms to a national referendum. One of the major complaints of students and opposition political forces has been the government's refusal to spell out a timetable for amending the constitution and holding a presidential election.

A promise that the government would abandon its own efforts to draft a new constitution and leave the job to the National Assembly. The opposition objects to the amendments being drafted by the government, which contains many long-time associates of Park. Government spokesmen said today that the National Assembly's version would be respected "to the maximum degree."

A pledge to lift martial law by a fixed date if the unrest subsides. That could be the most ticklish task and sources said it is unclear whether the government would go that far.

These three issues have become the focus of student demonstrations. The students and many opposition politicians believe that the government's persistent vagueness on all of them is part of a plan to restore some of Park's authoritarianism and keep some of his friends in office.

A public statement spelling out the concessions is expected as soon as President Choi Kyu Hah returns from a state visit to two Middle East countries. In his absence, Prime Minister Shin has held daily meetings on the crisis and shared in drafting the government's statement, but he is leaving its announcement to Choi.

According to reliable sources, the government's main concern is to avoid the appearance of capitulation to student protests. Early this week, it unexpectedly agreed to convene a special session of the National Assembly next Tuesday. The formal announcement may not come until the legislature convenes, the sources said.

The New Democratic Party, the principal opposition party, has already voted to promote a legislative resolution calling for an end to martial law, imposed last October when Park was slain. If it passes the assembly next week, President Choi must either lift martial law or present precise reasons for keeping it, something the government has been unwilling to do.

The huge waves of student demonstrators marched today into the central city from four gathering points, chanting political slogans and shouting demands that key government officials and military leaders resign.

They marched unmolested for blocks in many cases, but at key intersections were greeted by massive barrages of tear gas. They responded by hurling bricks and sticks.

In a typical rally, thousands of students led by a core of demonstrators from Dong Guk University headed down a main thoroughfare not far from the center of government buildings and about two miles from the Blue House, the presidential mansion.

At one intersection, they were met by dozens of canisters of tear gas and a huge, swirling cloud of pepper fog discharged from police vans. They retreated, regrouped, charged forward and ran into another tear-gas barrage.

They carried signs demanding an end to martial law and the ouster of Gen. Chon Doo Hwan, a military leader newly powerful as director of the Korean Central Intelligence Agency.

Meanwhile, officials reported that North Korean intruders exchanged fire with Americans manning a U.N. guardpost near the Demilitarized Zone separating the North and South. No injuries were reported. It was the second border incident in two days.