Thousands of Iranian women braved gunfire, beatings and insults today in new street demonstrations protesting against fundamentalist Islamic efforts they fear will reduce them to the status of second-class citizens.

For the second time in three days militant women defied the authority of Ayatollah Ruhollah Khomeini.

Iran's unofficial head of state is also under attack from a vocal minority made up of liberals, leftists and lay Iranians, all of whom are fighting what they denounced as his dictatorial tendencies.

Women demonstrators who converged on the Justice Ministry to protest against the "new tyranny" scored a victory of sorts when the carefully supervised government-run radio read out their demands.

The demands ranged from equal political, economic educational and civil rights for both sexes and guarantees for jobs now held by women to free choice in clothes rather than imposition of the full-length chador favored by the Moslem zealots.

The women had threatened to demonstrate again Sunday unless their demands were broadcast, and feminist sources predicted the agitation would continue in any case through Monday.

Throughout the march, protected by friendly men, the women came under heavy verbal abuse. Some women were reportedly attacked with knives, stones and broken bottles by angry men.

At one point, Islamic militia men near the Soviet Embassy fired in the air to prevent a major confrontation between the mainly middle-class women and their often poorly educated, but clearly furious, detractors.

In an indication of government concern lest the women's protest prove contagious, the radio kept broadcasting the public prosecutor's warning that anyone caught abusing women would be considered counterrevolutionary.

Several news agencies said anonymous callers had warned that women would immolate themselves if Khomeini did not come out squarely guaranteeing their personal liberty.

Newspapers reported cases of women secretaries being turned away by Moslem zealots when they showed up for work on grounds they were indecently dressed. They were told to return home and put on a chador or head scarf.

Sources close to Khoemini in Qom, the holy Shiite city 90 miles south of Tehran, where the ayatollah set up residence last week, suggested that he had never meant to impose the chador as long as women's hair, legs, arms and feet were covered.

It was Khomeini's own denunciation of "naked" women that spurred the current militancy among women. They are angered by what they suspect is the handwriting on the wall involving "suspension" of legislation protecting them against arbitrary divorce and bigamy. The "suspension" has also had the effect of banning coeducation and abortion.

Ayatollah Mahmoud Talaghani, Khomeini's surrogate in Tehran, insisted no force would be employed to insure the wearing of the chador.

But in a broadcast he said Moslem women always had worn some sort of veil and warned "since everyone believes in the imam (Khomeini) as a leader and father, they must take his advice."

Meanwhile, the death early Thursday morning of one Soviet engineer -- and the wounding of another -- was confirmed. They were shot near the Soviet Embassy by Islamic militiamen apparently when their car failed to heed a roadblock.