MOSCOW, FEB. 24 -- Soviet officials today moved to quell continued demonstrations in Soviet Armenia by naming an Armenian to head a region claimed by both Armenians and a rival ethnic group in the neighboring republic of Azerbaijan.

Faced with protests that local dissidents said involved more than 100,000 people today, communist leaders in the disputed region of Nagorno-Karabakh ousted Boris Kevorkov as party chief and replaced him with Genrikh Pogosyan.

Tass announced Pogosyan's appointment at the end of the fifth day of protests in Yerevan, the capital of the Armenian republic. Party officials "have considered urgent measures" to normalize the situation there, the official news agency said. It gave no details.

The demonstrations started two weeks ago in Stepanakert, the capital of Nagorno-Karabakh, and spread last week to Yerevan as Armenians in both cities protested the Kremlin's 1923 decision to divide them by setting up an autonomous region in Azerbaijan.

Protesters tonight were reported to be in the streets of cities throughout Armenia.

The protests followed a steady increase of tensions between Armenians and Azerbaijanis in Nagorno-Karabakh. Armenians, who form the majority of the region's population of 160,000, have accused Azerbaijan's leaders of religious discrimination and attempts at cultural domination.

Armenian dissidents leading the protests in Yerevan and Stepanakert did not comment publicly on the appointment of Pogosyan. In a telephone call from Yerevan, however, Armenian nationalist leader Paruyr Ayrikyan said that the crowds had grown despite a plea from the Armenian Communist Party chief for them to disperse.

Standing in an apartment overlooking the protests, Ayrikyan estimated that more than 100,000 Armenians had gathered in the streets today. The figure could not be confirmed independently.

The Armenian protest, one of the largest ethnic outbursts ever in the Soviet Union, is among several recent nationalist demonstrations and poses a major test for the Kremlin, which is balancing efforts at liberalizing Soviet society while maintaining firm political control.

In recent months, ethnic groups in some outlying Soviet republics have questioned the Kremlin's policy on nationalities and the Communist Party's authority with increasing boldness and have become the object of carefully orchestrated crackdowns.

A demonstration against Soviet rule in Estonia was called today in the capital of Tallinn and several other cities, but the telephone lines of Estonian activists were cut and the official Soviet media reported only a counterdemonstration organized by the local party protesting alleged Reagan administration interference in Estonian affairs.

In a telephone call from the Estonian city of Tartu, activist Albert Turpu said attempted protests were thwarted by police and that he had been taken from a friend's home by armed militia this afternoon and detained for six hours.

{Estonian sources in Stockholm said they had reports that 20,000 to 30,000 demonstrators gathered Wednesday night in Tallinn's streets despite television announcements warning against the protest. The sources said that authorities were using sound trucks and sirens to drown out the demonstrations, but that Soviet militia apparently had left the capital's streets. The Stockholm reports could not be verified immediately.}

In Armenia, the party has taken a more compromising approach. Two Kremlin officials, party secretary Anatoly Lykyanov and Politburo member Vladimir Dolgikh, flew to Yerevan from Moscow to handle the affair and today summoned 80 leaders of the protest to a meeting in an attempt at mediation, Ayrikyan said.

Armenian dissidents in Moscow also interpreted the firing of former Nagorno-Karabakh party chief Kevorkov as a concession to the protesters. Kevorkov was dismissed for "shortcomings in his work," Tass said.

A meeting of party activists in Stepanakert criticized the Armenians' protests, however. Their actions and demands "do damage to inter-ethnic relations," Tass said. Unless responsible measures are taken, the situation might result in irreparable and "unpredictable" consequences, Tass added.

Ayrikyan, who spent 17 years in Soviet labor camps for helping found the Armenian nationalist party in the late 1960s, said he and other activists had spoken at the demonstration in the center of Yerevan.

He said the protesters have dispersed every evening at 11 p.m. and gathered again at 9 a.m. to comply with a local city council rule outlawing demonstrations there at night.