While opposition mounts in Canada to a recently completed free trade agreement with the United States, other countries are asking the Reagan administration for a chance to conclude similar pacts.

Among major U.S. trading partners that have expressed interest in negotiating free trade pacts with the United States are Japan, South Korea, Taiwan and some members of the five-country Association of Southeast Asian Nations (ASEAN), especially Singapore. In addition, Israel now wants its two-year-old free trade agreement upgraded to match some of the provisions in the Canadian pact, administration trade officials said.

These countries want the agreement for the same reasons that led Canadian Prime Minister Brian Mulroney to propose the idea to President Reagan 2 1/2 years ago: the possibility of shielding themselves from U.S. unfair trade laws, which most countries see are growing increasingly protectionist, while obtaining U.S. acceptance of some of their own practices that skirt trading rules.

The Canadian arrangement, for instance, contains a section that enshrines Canada's protection of its entertainment, broadcasting and publishing industries to maintain its cultural differences from the United States. It also includes a special dispute settlement mechanism that Israel would like added to its agreement.

The agreement with Canada is far less sweeping than originally envisioned by Mulroney and Reagan, but it has won general support in the United States as a major free trade move in a time of growing international protectionism. Despite complaints about certain areas such as the protection of Canada's entertainment industries and a perceived advantage given to its auto industry, Congress is expected to approve the agreement.

In a speech to 180 business leaders who were briefed on the free trade pact Wednesday, President Reagan hailed the agreement as "another great leap of progress ... tearing down the walls, the tariffs that block the flow of trade, and eliminating the tangle of restrictions and regulations that bind our commerce and inhibit economic cooperation."

But the agreement has ignited a firestorm of opposition in Canada based on arguments that it would cost jobs and allow U.S. domination of the Canadian economy. Last month, for instance, Canadian union chiefs appeared at the AFL-CIO convention to enlist the aid of U.S. organized labor in fighting the pact, saying it is not good for workers in either country.

Still exhausted from the Canadian negotiations and with the pace of global trade talks in Geneva heating up, the Reagan administration has been fending off the advances of other countries.

U.S. Trade Representative Clayton K. Yeutter acknowledged in a speech in Singapore eight days ago that "other nations, including some in ASEAN, have expressed interest in being the next partner in a free trade arrangement with the United States."

He said, "We appreciate these expressions of interest because we seek increased global trading opportunities whenever possible, but it is premature for us to consider entering into another negotiation at this time."

In the closed portion of Wednesday's briefing for business leaders, Yeutter was asked about future agreements. He said he was "conceptually favorably" disposed to them, but the administration will have to decide which country or group of countries should be targeted.

Deputy U.S. Trade Representative Michael B. Smith made the same points when asked in September about the possibility of a free trade agreement with South Korea. "Our plate is pretty full," he said.

But both Yeutter and Smith hold out the possibility of future talks to arrange free trade agreements with selected countries, especially if there is a breakdown of negotiations to strengthen the international compact that regulates world trade, the General Agreement on Tariffs and Trade (GATT).

The set of GATT talks under way in Geneva, known as the Uruguay Round after the nation where the meeting that kicked them off was held, form a cornerstone of U.S. trade policy. But U.S. trade officials believe that if the 40-year-old GATT is not strengthened to meet the new trade problems of the 1990s and beyond, the United States might be better off with a series of bilateral arrangements that ultimately could form the basis of a stronger international trade organization.

Yeutter went out of his way in the Singapore speech, however, to reassure other trading nations that the U.S.-Canada pact "is not a retreat into bilateralism or managed trade." He asserted, "It will complement the GATT negotiations and serve as an important model for many Uruguay Round negotiating areas."

Singapore Ambassador Tommy T.B. Koh said Prime Minister Lee Kuan Yew proposed a free trade pact to the Reagan administration when he visited Washington two years ago, but was told the United States would rather deal with the ASEAN nations as a group. Reportedly, however, some ASEAN members are not ready for such an arrangement.

As one of the few completely free-trade countries in the world, Singapore still would like to conclude a separate pact with the United States, Koh said, but he added that there is little his country, with its open markets, could offer. He suggested that the free trade pact could be used as a carrot to benefit countries that maintain free markets.

Taiwan's desire for a free trade pact, being pushed quietly in this country by its diplomats and businessmen, received a boost in September when the director of the Heritage Foundation's Asian Studies Center, Martin Lasater, endorsed the idea.

In Japan, Ambassador Mike Mansfield proposed that the United States and Japan negotiate a free trade pact based on reciprocity. He emphasized that he was floating the suggestion on his own, not speaking for the Reagan administration, and said the agreement would end "this nickel and diming" approach that has raised tensions in a whole series of trade disputes between the two countries.

"The problem is that we've been trying to bring about accommodation and reform and compromise in a bits-and-pieces manner, nitpicking here and there," the 84-year-old ambassador was quoted by the Associated Press as telling a group of Japanese businessmen recently.

The idea has been picked up and modified by a former official of Japan's Ministry of International Trade and Industry, Akira Harada, who said in a New York speech last month that a free trade pact would "refresh and revitalize America and Japan" and "provide further momentum to strengthen the ties" between the two countries.

Harada, now a senior adviser to Matsushita Electric Industrial Co., would exclude agriculture -- a politically sensitive sector in Japan -- and thus shelter that nation's protectionist farm policy. In return, he said Japan could exempt textiles, steel, machine tools, automobiles and semiconductors, which he said were important to the United States.

The United States also is forging closer trade ties with Mexico. Yeutter signed an agreement in Mexico City on Friday that falls far short of a free trade relationship, but is considered a major move for the two countries because it sets up a framework for consultations on trade issues before they grow into disputes.

Yeutter called it "step one" of many steps that could lead to a hemispheric arrangement involving the United States, Canada and Mexico, long a dream of President Reagan.

While other countries are trying to strengthen trade ties with the United States, Canadian public opinion has turned against the free trade agreement and the political opposition has mounted a major campaign to kill it.

A poll late last month by the Toronto Globe and Mail and Environics Research Group Ltd. showed that public support for the agreement has slipped to its lowest level in 3 1/2 years and more people than ever are uncertain about its benefits. The poll showed that a bare 49 percent of Canadians supported the pact, a decrease of 7 points since June, while 34 percent -- the same as June -- opposed it. The undecided group went up by 7 percentage points, to 17 percent.

Since the basic agreement was reached just before a midnight deadline on Oct. 3, opposition in Parliament has grown fiercer. Liberal Party leader John Turner said he would like the next general election, which Mulroney is expected to call within a year, to be a referendum on the agreement.

Since proposing a free trade pact as a keystone of his economic policies, Mulroney has seen his political star wane, and his Conservative Party has lost ground in the polls as the Liberals and the socialist New Democratic Party have moved into the lead.

Ed Broadbent, the NDP leader, said he would not honor the agreement if his party wins power, and he has threatened delaying tactics in Parliament to press Mulroney to call a quick election. The ruling Conservatives hold 208 of the 282 seats in the House of Commons.

Turner is especially upset because Mulroney failed to win the full exemption from U.S. unfair trade laws that he sought. "Without an exemption from American trade law, the agreement is not worth the paper it's printed on," the Associated Press quoted Turner as saying.

In addition, three of Canada's 10 provinces, whose assent is necessary to put parts of the pact in action, are opposed to the agreement.

Trade Minister Pat Carney, defending the agreement during a daylong Parliamentary debate in Ottawa late last month, said a free trade agreement represents the future for Canada while the opposition represents the past.

"Canadians have just heard from the 19th century," she said after Turner's speech.