MOSCOW, JULY 2 -- U.S. special envoy Vernon Walters declared success today in the first round of his mission to end the seven-year-old Iran-Iraq war, saying that the United States "can count on" Moscow's vote for a United Nations resolution demanding a cease-fire.

Following a day of talks with senior Soviet Foreign Ministry officials, Walters said that the Soviet Union and other key U.N. countries have shown "a greater desire to be successful on this particular issue than I have found in any of the previous discussions I have had before."

But Walters, in a press conference at the American Embassy, hinted at disagreements over a second U.S.-backed resolution that would impose mandatory sanctions, including an arms embargo, on whichever country refused to comply with a U.N.-ordered cease-fire.

"Obviously we have been thinking about what we should do if the deal is rejected," he said, declining to elaborate.

{U.S. Ambassador Jack Matlock this week gave Soviet leader Mikhail Gorbachev a message from President Reagan asking for support on both the cease-fire and sanctions resolutions, White House spokesman Marlin Fitzwater said in Washington. He said Reagan sent similar messages to leaders of the three other permanent members of the Security Council -- Britain, China and France.}

The Soviet Union, which maintains close ties with both Iran and Iraq, may be reluctant to agree to strong enforcement of a cease-fire, Moscow-based western diplomats who specialize in Mideast affairs said today.

Walters said that the five permanent members of the Security Council support the cease-fire resolution. "So far we think we can count on those votes for such a resolution," he said.

But Walters acknowledged that the Security Council's nonpermanent members have not yet responded.

"Unanimous support," he said, "would carry the greatest weight and have the greatest impact on the warring parties," adding that the nonpermanent members, now studying the draft resolution, should report back within the next two weeks.

Walters arrived in Moscow on Tuesday, the same day Reagan announced that the United States was beginning a diplomatic initiative to end the war, which started in 1980.

Walters told journalists that he was under instructions from Reagan "to discuss this matter very carefully with the Soviets, to explore the areas where we could work together to put an end to this killing."

Walters said that the four hours of talks he held today with senior Foreign Ministry officials had centered on the the war in the Persian Gulf, but included other issues.

Walters met with Deputy Foreign Minister Vladimir Petrovsky and other ministry officials. Following further talks here Friday, he plans to depart for consultations on the gulf with Chinese officials in Beijing before reporting back to Reagan.

Both the United States and the Soviet Union are involved in efforts to protect Kuwaiti tankers from Iranian attacks. U.S. officials have accused China of selling Iran Silkworm missiles that Washington says threaten shipping in the gulf.

Asked whether he and Soviet officials had discussed measures to force Iran and Iraq to accept a cease-fire, Walters said, "We discussed all aspects of this question. Without getting into too much detail, I think everybody agrees that something has to be done."

Walters, who is U.S. ambassador to the United Nations, pointed out that the world body has passed various resolutions on the Iran-Iraq war, saying that "none of them has succeeded," and adding that they have all requested a cease-fire. "This one would demand it," he said. "That's the difference."

President Andrei Gromyko pledged Soviet support for the resolution in a Kremlin meeting with Iraqi First Deputy Prime Minister Taha Yassin Ramadan, the Soviet news agency Tass reported.

"The United Nations, its Security Council, are called upon to play an important role in the effort exerted now for an early end to the senseless bloodshed," Tass quoted Gromyko as saying during the meeting. Ramadan said that Iraq is "closely following" the drafting of the resolution.