A senior member of the Iraqi leadership arrived here Thursday on an unannounced mission apparently seeking Soviet political and military assistance for the embattled government of President Saddam Hussein.

But the apparently cool reception accorded to Iraqi Deputy Premier Tariq Aziz suggested Moscow's extreme caution following recent Iranian victories in the Persian Gulf war and little prospect of any Soviet arms deliveries to Iraq.

The Soviet media so far have not even reported his arrival. Iraqi sources here said that by midafternoon yesterday, or 24 hours after his arrival, Aziz had not met with a single Soviet official.

Soviet-Iraqi relations have deteriorated over the past two years despite a 1972 treaty of friendship and cooperation. Under the agreement, the Iraqis could seek Soviet assistance should Iran send its forces across the border into Iraq.

Since Saddam Hussein launched his attack on Iran, the Russians have maintained an evenhanded approach toward the belligerents and have refused to supply Iraq with weapons. Moreover, in steps that reflected Iran's greater importance to Moscow, the Russians have sought to cultivate a new relationship with Tehran by skirting political differences and focusing on economic relations instead.

In the only public comment since Iran's recent victory at Khorramshahr, the Communist Party newspaper Pravda said that "the further escalation of fighting, for example its transfer to the territory of Iraq that has recently begun to be discussed, could draw more countries into the war."

But the commentary contained no hints of possible Soviet involvement.

Syria, Moscow's pivotal ally in the Arab world, has come out openly in favor of Iran. So did the other members of the Steadfastness Front--Algeria, Libya, South Yemen and the Palestine Liberation Organization--all of which have close relations with the Soviet Union.

Other Arab states including Jordan, Egypt and Saudi Arabia are supporting Iraq.

The Kremlin has maintained that Iraq and Iran should settle their differences through negotiations and that their conflict has left them "estranged from the active struggle against the intrigues of imperialism and Zionism."

The Russians, however, see a broader danger in the spread of Moslem fundamentalism. It has been the rallying point for the opposition to Syrian President Hafez Assad during recent fighting in Syria.

According to Western diplomats, the Russians have sent a number of officials and experts to Middle Eastern countries during the past three months in an effort to assess uncertainties in the region.

First Deputy Premier Ivan Arkhipov last week visited Syria, reportedly to prepare a visit by Assad to Moscow either later this month or next October, according to diplomatic sources. Assad is said to want to broaden the Soviet-Syrian friendship and cooperation treaty to include firm Soviet pledges of military support for Syria if Israel were to attack Lebanon.

There was speculation here that Aziz's mission may be to seek Moscow's moderating influence on Syria.