A top Iraqi official briefed senior Kermlin advisers on the Iraq-Iran conflict today, amid strong signs that the Soviets are not eager to take sides and only hope the sudden border clashes in the volatile Persian Gulf region will die down quickly.

Tareq Aziz, a close adviser to Iraqi President Saddam Hussein and member of the ruling Revolutionary Command Council, opened two days of speedily arranged talks here with a session with Communist Party Secretary Boris Ponomarev, and Viktor Maltsev, a Central Committee member and deputy foreign minister.

The official Tass news agency said the men discussed "topical questions of the present international situation and the situation in the Near and Middle East."

Observers here say the opaque language is a good indication of Moscow's discomfiture at the outbreak of hotilities, which threaten harm to the complex relationships Moscow has achieved -- or seeks -- with the two oil-rich countries Baghdad signed a friendship treaty with the Soviets in 1972; the Kremlin is its principal arms supplier and a major trading partner. Nevertheless, Moscow badly wants improved relations with Iran, in part because Tehran early this year ceased shipment of natural gas to the Soviet Union, crimping its own supplies and hard-currency gas sale.

Reflecting the worry over impairing relations with either combatant, the official Soviet media has been largely silent about the artilery, air and naval clashes of the last few days. The Communist Party daily Pravda, in what is the only extended comment to date, today accused the United States of setting the two countries against each other "following the principle of divide and rule."

The Soviets see the fighting as a divisive and dangerous distraction from the Arab confrontation with Israel and the United States. Tas tonight quoted an Arab League official, Chedli Klibi of Tunisia, as saying the "present events threaten to develop into a war between the two countries and this pains Arabs. We want a normalization of relations . . ." between the two.

Soviet influence in Baghdad, high in the late 1960s after the Baathists came to power, has diminished slowly sonce. 1973, when zooming Arab oil revenues brought some independence to Saddam Hussein from Moscow policies and helped free him to challenge Iran for regional supremacy. The 1978 executions of 21 newly communist military officers gave Moscow a severe shock, but the two capitals have continued generally good relations.

Meanwhile, Moscow has continued its attempts to improve relations with Ayatollah Ruhollah Khomeini's Islamic government, making some recent gains, but taking some setbacks as well. Just last week, Tehran and Moscow signed a new transit agreement that could bring a doubling of rail traffic between the two countries.

Two days ago, however, the Soviets were forced by the Iranians to close the Soviet Consulate in the Iranian city of Right in the Caspian Sea, Two months ago, Moscow refused the Iranians permission to open a consulate in Dushanbe, Tadzhikistan. The Iranians have closed their Leningrad mission and retain a consulate in Baku, the Capital of Soviet Azerbaijan.

The Dushanbe refusal is seen here as reflecting Soviet concerns about the impact of the Islamic fun-damentalism of Khomeini's government on this country's own Moslem population, which numbers about 50 million. Tehran has openly promulgated its religious militancy, and like Baghdad, bitterly denounced the Soviets for invading Afghanistan to quell the anti-Marxist Moslem rebellion there.