In deciding to convene a summit on the Persian Gulf crisis and other topics, President Bush and Soviet President Mikhail Gorbachev are once again offering definition to the goal of a new world order based on superpower cooperation rather than competition.

Ever since Iraq's invasion of Kuwait, the Soviet Union has joined the international community in opposing the aggression of President Saddam Hussein and supporting the global embargo against him, even though Iraq was a longtime friend and weapons customer of Moscow. Now this international solidarity against Saddam may be underscored in an even more dramatic fashion as Bush and Gorbachev meet next Sunday in Helsinki to talk about the confrontation.

"This is an opportunity at a time of crisis in which we are both working hand in glove for the two leaders to get together and cement that coordination and send the rest of the world a very important signal," a senior administration official said.

The signal is that Saddam is not just facing the United States, but the entire global community, and that he cannot hide behind the pretext that some nations condone his aggression, the official said.

In that respect, the Helsinki summit is designed to amplify the joint call for Saddam to retreat that Secretary of State James A. Baker III and Soviet Foreign Minister Eduard Shevardnadze made in the first days of the crisis.

Bush said yesterday "we have many matters to discuss," and U.S. officials said there are a host of other topics demanding the attention of the president and Gorbachev. Among them are the strategic arms reduction treaty, which both leaders promised at the May 30-June 3 summit in Washington to try to finish this year. However, the negotiations have been virtually stalled, according to some reports. Another major agenda item could be a settlement of the Afghanistan conflict, on which both sides are moving toward a formula for disengagement and a transition to elections. Other issues they may address are the negotiations on reducing conventional forces in Europe and a framework agreed to by the five permanent members of the United Nations Security Council for settling the conflict in Cambodia.

Ever since the collapse of the Berlin Wall last year and the easing of Cold War tensions, there has been a debate about what kind of world order would arise in the vacuum left by the waning superpower conflict. One of the great fears about this new environment has been that, with the superpowers ostensibly turning inward, new regional conflicts would flare. It was just that kind of conflict that Saddam Hussein touched off with the Aug. 2 invasion of Kuwait.

Thus the Helsinki meeting could help define the post-Cold War order if both Bush and Gorbachev show at the outset of this period that they are prepared to stand firm against such regional outbursts and if this pressure succeeds in hastening an end to the crisis.

For Gorbachev, there is a larger stake. In the months ahead he is facing another difficult drive to implement radical economic changes, and the wealthy Western nations are now conducting their own studies of his needs and whether to provide the Soviets with more aid. He is also beginning what could be an agonizing internal effort to cope with his country's restive nationalities and the push by some of the 15 Soviet republics for greater autonomy or outright independence.

More than anything, Gorbachev may hope that he can demonstrate in this crisis that the Soviet Union should qualify for additional cooperation with the West because of its "good citizenship" in helping the rest of the world face down Saddam.

While Gorbachev has joined the international outcry against the invasion, his approach has been to emphasize the importance of diplomacy and the role of the United Nations and to play down military conflict. Some Soviet officials have voiced concern about the big American military buildup so close to Moscow's borders. "You have a Soviet public that is still traumatized by Afghanistan," said a U.S. official familiar with the extensive contacts in recent weeks with Moscow. "Given their problems, they are not looking to invite military intervention."

The Soviets have been evacuating their citizens from Iraq but have acknowledged the presence of 193 military trainers still in Baghdad. Soviet officials have insisted they are not combat advisers but under contract to train Iraqis in the use of weapons. U.S. officials have raised questions with Moscow about the trainers, but one source said it has not become a major issue. "It is not simply a black and white case," the U.S. official said. "They are thinking about the safety of their citizens. If they pulled all the advisers out, what would that tell Saddam?"