MOSCOW, FEB. 28 -- The suspension of mass protests in Armenia yesterday has given Soviet leader Mikhail Gorbachev a month to settle a problem whose solution eluded his predecessors: how to satisfy restless nationalities while maintaining the Kremlin's control.

By temporarily halting the biggest street protest in Soviet history, the demonstrators intensified a debate on whether Gorbachev's policy of glasnost, or openness, and an expanded tolerance of demonstrations, has gone too far.

Controlling restive nationalities, an issue since the Soviet Union was formed 70 years ago from disparate ethnic and language groups, has become Gorbachev's most pressing domestic problem.

Its importance was underscored by the Soviet leader's unusual appeals for calm in a letter read Friday on Armenian and Azerbaijani radio and television and in an unannounced Kremlin meeting with two Armenian writers that led to the one-month suspension of protests.

Nationalist tensions are a major issue in nearly all of the 15 Soviet republics. Eruptions have occurred several times since Gorbachev took office. The nine days of demonstrations in Yerevan, Armenia, followed nationalist-inspired riots in the Kazakhstan capital of Alma-Ata in December 1986, protests in July 1987 by Crimean Tatars displaced from their homeland, and separatist rallies across the Baltic republics since last spring.

In the Baltics, where anti-Russian feelings run strong, the demonstrators are fighting a losing battle against Soviet rule.

In Armenia and the neighboring republic of Azerbaijan the dispute is over whether Nagorno-Karabakh, a small mountainous region that became part of Azerbaijan by Kremlin decree in 1923, should become Armenian.

Since the Armenian protest began in Yerevan on Feb. 18, it has revealed ethnic pride at its extreme. For more than a week, hundreds of thousands have stormed through the city, chanting, carrying posters, and delivering speeches. The object, as one popular banner put it, was to demand that Moscow "Give us Nagorno-Karabakh."

The disputed region's population is about 160,000, at least 75 percent of whom are ethnic Armenians. There is a religious element in the dispute as the Azerbaijanis are largely Moslem and the Armenians Christian.

Under Gorbachev's predecessors, the protest would likely have been crushed or news of it censored. Joseph Stalin's solution to nationalities squabbles was terror tactics, while Leonid Brezhnev's was selective repression. In 1979, after leaflets circulated in Yerevan criticizing Brezhnev and Soviet authorities, KGB agents arrested a leading Armenian activist and tried him for anti-Soviet activities.

As for tensions between Azerbaijanis and Armenians in Nagorno-Karabakh, a native of the area recalled an incident in which an Azerbaijani school director in the city of Stepanakert killed an Armenian student and was brought to trial.

When an Azerbaijani judge gave the director a light sentence, the Armenians burned a car holding the killer, the judge and some others. Other violent incidents took place in 1968 and 1972-73 but "nobody heard much about them," the Azerbaijani said in an interview, "because there was no glasnost."

So far, Gorbachev's approach to the nationalities issue has been mixed. By taking his campaign for restructuring to outlying provinces -- where it has been resisted with a vengeance -- he also has touched on issues of nationality.

In a speech last June, for instance, he charged the Communist Party leadership in Yerevan with complacency. Identifying party boss Karen Demirchyan as a key culprit, Gorbachev said that "a totally unjustified tranquility is being shown." He added that "no effective efforts are being made against bribery, profiteering, and protectionism."

Two years ago, Gorbachev delivered a similar attack against Kazakhstan party chief Dinmukhamed Kunaev, starting an all-out campaign that resulted in his ouster and replacement with an ethnic Russian. The public reaction -- two days of riots in Alma-Ata that left three dead and dozens wounded -- apparently has left a mark on Gorbachev's nationalities policies.

Last summer, Crimean Tatars demonstrated in front of Lenin's tomb and then tried to storm Red Square to demand that their homeland on the Black Sea be returned to them. The result was a senior-level commission to study their demands. "We don't think these things should simply be shoved under the rug as they were in the past," an official said at the time.

Western diplomats here say, however, that the persistence of Armenian demonstrators could strengthen the resolve of Kremlin hard-liners to crack down eventually. Following nationalist-inspired demonstrations in the Baltic capitals of Riga, Tallinn and Vilnius last August, activists there have met with expulsions, detentions, and house arrest.

Two weeks ago, in a major speech on other issues, Yegor Ligachev, by reputation the leading conservative in the ruling Politburo, attacked ethnic nationalists, including Baltics, Siberians and Kazakhs.

The Armenian dispute could be used by party conservatives to argue that Gorbachev's policy of glasnost has run amok. The party's Central Committee already has voted to reject the proposal that Nagorno-Karabakh be joined with Armenia, according to Tass, the official news agency.

For the 3.4 million Armenians and others of the 17 major Soviet ethnic groups, the demonstrators are viewed as a test of whether glasnost ultimately serves their interests. Gorbachev would lose support among them if he fails to find a compromise. So far, they appear to support him, however. One of the most popular posters carried at the demonstrations was of the Soviet leader beneath the words, "We trust you."

Still, leniency in the Armenia case could create a precedent that the Kremlin seems anxious to avoid. "If Nagorno-Karabakh is given to Armenia," a Soviet official said in an interview, "land on the Black Sea will have to be given to the Crimean Tatars and the process will never stop."