Canada and the United States are trying to forge a free-trade agreement that eventually would erase all tariff and nontariff barriers between the two countries, the world's largest trading partners.

"We have to do something to secure our access to the United States" markets and "protect ourselves" against restrictive trade legislation looming in Congress, Canadian Trade Minister James Kelleher told the Business Council at its biannual meeting here last week.

Kelleher, one of a group of foreign officials who were invited to the meeting, made up of executives of America's largest and most powerful corporations,, said he is studying three options for Canadian-U.S. free trade and will present his recommendation to the Cabinet next month. He said he hopes to start full negotiations with the Reagan administration by the fall so that negotiations can be close to an agreement before next year's congressional elections.

While Canada sees a free-trade agreement as a means of preserving its largest export market, the arrangement fits into the Reagan administration strategy of entering into bilateral trade pacts in the absence of global negotiations under the General Agreement on Tariffs and Trade (GATT).

The administration this spring concluded an agreement with Israel that would end all trade barriers between the two countries within 10 years. President Reagan hailed the agreement as a model for other trading partners.

In the wake of the inability of the Bonn economic summit to agree on a starting date for a new global round of trade talks, moreover, administration officials warned that the United States would hold its own negotiations with nations that wanted individual deals. While former U.S. trade representative William E. Brock, now President Reagan's Labor secretary, cited Pacific rim nations as appropriate countries for such deals, Canada also can be seen as meeting the criteria.

Canada last year held a $20.4 billion merchandise trade surplus with the United States, and the balance of trade seems headed in the same direction this year. Canada's merchandise trade surplus totaled $7.1 billion for the first four months of 1985.

But Kelleher said that "the deficit is not as bad as it looks" because Canada had a $14 billion deficit with the United States in trade in services, making its total surplus just $6.4 billion. Moreover, he said, Canada has run a trade deficit with the United States for eight of the past 10 years.

The effort to forge a free-trade agreement received a boost from the "St. Patrick's Day Shamrock Summit," when President Reagan and Prime Minister Brian Mulroney agreed that the two countries should seek ways to end trade barriers between them.

"The Canadian people seem to be very sympathetic and appear to be in favor of a comprehensive trade agreement with the United States," Kelleher said after an eight-week cross-Canada tour of 15 cities to sound out differing views on a possible free-trade agreement.

While not tipping his hand as to which proposal he will recommend to the Cabinet, Kelleher seemed to favor a comprehensive agreement that would cover most of the $120 billion in trade that passes between the two countries.

He said an attempt last year to negotiate free-trade agreements on a sector-by-sector basis was unsuccessful. "If one country's industry was for it, the other's opposed," he said. "The approach did not allow tradeoffs."

Kelleher listed two other possibilities: to allow the present situation to continue "and hope that the protectionist pressures in Congress can be contained," or to negotiate a broad agreement committing the two governments to removing barriers without any specifics.

As an indication of Canada's new mood on trade, Kelleher said Mulroney's government is moving to eliminate "such nationalist creations" as the Foreign Investment Review Agency (FIRA) and the National Energy Program, which were seen as limiting U.S. investment in Canada.

He said the biggest barrier to free trade between the two countries are "Buy America" and "Buy Canada" laws now on the books. For a Canadian company to get a contract to build subway cars for New York City, for example, it had to open a plant in Vermont because of "Buy America" provisions of the urban mass transit law.

"Quite honestly, we don't come with clean hands, either. We have the same legislation. We're not Girl Guides," Kelleher said.

The major trade friction between the two countries now concerns lumber, an area in which Canada holds about one-third of the U.S. market. Legislation is about to be introduced in Congress that would limit Canadian supplies, and Kelleher said that he and former U.S. trade representative Brock held monthly meetings on the lumber issue.