MOSCOW, JULY 24 -- The Soviet government has agreed to reexamine the claims of Crimean Tatars to their homeland on the Black Sea, officially reopening a painful issue that dates back to one of the darkest episodes of World War II.

In naming President Andrei Gromyko to head a study commission on the question, the Kremlin responded to a renewed campaign, supported by leading cultural figures, for the restoration of the Crimean Autonomous Republic. The republic was abolished in 1944 by Soviet leader Joseph Stalin, and an estimated 500,000 Crimean Tatars were forcibly resettled in Central Asia on blanket charges of collaborating with the Germans.

Crimean Tatar activists, many of whom were in Moscow this week staging demonstrations for their cause, greeted the announcement with caution. This morning, 100 demonstrators again held a peaceful protest outside the offices of the Communist Party Central Committee, demanding to meet General Secretary Mikhail Gorbachev. In recent weeks, the group has staged demonstrations in Red Square, and has been invited to meet with officials of the Presidium and Central Committee.

The announcement of the government commission repeated the charges of Tatar collaboration with the Germans during the Nazi occupation of the Crimean Peninsula and claimed that Tatar nationalists had participated in atrocities .

"But unfortunately the decision of the State Committee for Defense on the eviction of the Tatar population from the Crimea was applied not only to the traitors, but to the entire Crimean Tatar population," said the announcement distributed by the official news agency Tass. ". . . the act of the wholesale eviction of the Crimean Tatar population was not just."

The Crimean Tatars are one of two Tatar groups in the Soviet Union. The other, larger group lives in the Tatar Republic on the Volga River. The Tatars are Moslems, descendants of the Golden Horde that swept across Russia in the 13th century.