HOUSTON, JULY 9 -- Leaders of the major Western democracies began their 16th annual economic summit today with preliminary agreement to launch a comprehensive study of the Soviet economy in response to appeals for financial aid from Soviet President Mikhail Gorbachev.

The agreement came as President Bush welcomed the leaders of the summit nations here, saying that "a new world of freedom lays before us." At a ceremony in near 100-degree heat at Rice University, where the summit sessions are being held, Bush challenged the leaders "to work toward decisions . . . that will bring new stability and prosperity to the world."

But decisions among the seven nations -- Britain, West Germany, France, Italy, Canada, Japan and the United States -- are likely to be difficult on several complex issues, including agricultural trade subsidies and international environmental cleanup.

Those issues were taken up at this afternoon's first plenary session, with the participants expected to hold further talks on the Soviet aid question later.

The issue of aid to the Soviet Union, initially expected to be one of the most contentious at the three-day meeting, appeared to be moving toward amicable resolution, at least for the time being.

Finance ministers, meeting earlier in the day, agreed to recommend to the leaders a study of Soviet needs by such international economic and lending organizations as the International Monetary Fund and the World Bank. Spokesmen for various governments said they also expected the fact-finding team to include representatives from the Organization for Economic Cooperation and Development, a Paris-based group of industrialized nations.

The idea of a study falls far short of the $15 billion direct Soviet aid package advocated by West German Chancellor Helmut Kohl and supported by France. But German officials appeared willing today to continue their own bilateral aid plans for Moscow, and to go along with the study -- as long as it is expedited -- as a first step toward an eventual multinational aid program.

The United States has opposed direct aid to Moscow not only on economic grounds, saying the Soviets must first make their economy more market-oriented, but also on defense and foreign policy grounds. Washington has objected to Soviet aid to Cuba and on certain nuclear weapons modernization issues. Japan, Canada and Britain have generally supported the United States.

The aid discussion was made more urgent by a July 4 letter Gorbachev sent to Bush, as host of the summit, in which he appealed for Western help to sustain his troubled perestroika reform program.

"We are now at a critical stage of perestroika, which calls for radical measures to sustain our changes," Gorbachev wrote, according to informed sources. "Our internal transformation requires external financial and economic help. We need in particular assistance in terms of long-term credits, which should be provided by foreign capital."

In their presentations today in a bilateral discussion between Kohl and Bush and in the meeting of finance ministers, the West Germans said that there was agreement on the analysis, but that Bonn insisted that "it must be immediate," and that a specific reply to Gorbachev's appeal should be made.

A senior aide to British Prime Minister Margaret Thatcher said the response would be a qualitative -- but not quantitative -- agreement to help. The seven leaders, he said, would reply: "Mr. Gorbachev, we want to help you." The aide continued, "The only argument is, how do we help you?"

The idea of delaying concerted Western action until further study was broached both by Bush and Canadian Prime Minister Brian Mulroney, who discussed it yesterday at their bilateral meeting.

White House press secretary Marlin Fitzwater said there was deep support among summit participants for perestroika. While Bush cautioned during today's session that the United States now is prepared only to provide the Soviets certain forms of technical assistance, Fitzwater said, "Our feeling is that individual countries are certainly free to follow their own dictates." This referred to U.S. acquiescence to an immediate bilateral German aid program that Bonn believes will help gain Soviet acceptance of German unification.

The proposal for a study of the requirements of the sinking Soviet economy would be the second such evaluation by the West now underway. Last month, the European Community (EC), which also is represented here by its president, Jacques Delors, ordered a study by Oct. 27. The EC study, prompted by Kohl's proposal, is an "aid exercise," said a senior U.S. official. "We're not yet ready to join that," he said, adding that this summit proposal is more focused on "the true financial condition of the Soviet Union."

IMF and World Bank participation in the study would not give the Soviets a much-coveted membership in the IMF. But the proposal reverses the administration's insistence that it is premature to involve the IMF in a relationship with the Soviet Union.

Among summit participants, the EC appeared least pleased with the study proposal. While welcoming the initiative as "quite a movement" in the previous U.S. position barring aid without fundamental Soviet economic reform, one EC official said the study would duplicate the European effort. "We want to keep the leadership on this issue in the European Community," the official said.

Other European officials, however, suggested the two studies could be merged. Thatcher's aide said Gorbachev already had written the British prime minister saying that he recognized the need to cooperate with such studies.