A compromise that appeared likely to end the bitter fight over the role of the Federal Trade Commission emerged yesterday after a meeting between congressional negotiators and President Carter.

Under the plan, the FTC could continue a number of major investigations, but would be forced to revise its controversial probe of television advertising directed at children.

The latest compromise, approved unanimously late yesterday by House conferees, would temporarily suspend the FTC's current children's advertising probe, but would permit the commission to vote to reopen it.

However, the FTC could only reopen the so-called "kid vid" case under a standard covering "false and deceptive" advertising, limiting the probe to advertising that is essentially inaccurate rather than misleading.

The FTC, under the compromise, would be able to conclude its rulemaking proceeding into pricing practices by the funeral industry, and its antitrust investigation of Sunkist, the giant agricultural cooperative, under some limitations.

The commission could also conclude an inquiry into the product and performance standards set by private industry boards, also under new limits imposed by Congress.

But the FTC would be forced to withdraw its petition to designate the Formica trademark as a "generic" product name which would be used by all suppliers.

Although the compromise must be approved by the full House and Senate, negotiators for the two houses said yesterday that the four-year-long struggle appeared over.

Sources said that yesterday's early-morning White House meeting set the stage for development of the latest compromise plan. President Carter took what sources called a "tough" position against Congressional actions to gut existing cases and complained frequently about his ideological problems about the two-house legislative veto, whic appears certain to emerge from the conference committee.

But rep. James Broyhill (R-N.C.), the ranking minority member of the House Commerce committee, insisted after the meeting of the House conferees that Carter "is just not going to get everything he wants.

"Presidents make a lot of statements like that, but they have to compromise," Broyhill said.

But FTC officials, including Chairman Michael Pertschuk, went out of their way to praise Carter's role in building an apparent concensus. "The American consumer and the FTC owe the president an enormous debt," Pertschuk said.

How the compromise would ultimately affect the Ftc's inquiry into children's television advertising was not clear yesterday.

Ftc sources said they believe the agency can pursue its case against "kid vid" advertising under the requirements of the compromise, since the advertising claims the FTC is concerned about can be attacked as "deceptive" as well as "unfair."

Nevertheless, lobbying continued throughout the day yesterday to tailor the final language of the bill in a way to block the FTC's "kid vid" case. Lobbyists for the sugar products industry were trying to have the children's advertising inquiry labeled "fundamentally flawed" in the final FTC bill, and require the commission to reopen the inquiry for further testimony.

Ford, the leading critic of the "kid vid" inquiry, said Congress would hold hearings to define the FTC's authority to regulate "unfair" advertising, noting that no new investigations on those grounds could be begun for three years. He said he thought that other industry groups that had feared becoming targets of such FTC actions would be reassured by the compromise.

Packwood, however, was disappointed by the outcome of the "kid vid" compromise. "Three principal groups want this bill changed -- the advertising industry itself, sugar and tobacco. They're getting their way," he said.

Another new proposal which surfaced in the House agreement called for the establishment of a panel composed of representatives of the FTC, and the Department of Agriculture and Justice to monitor FTC regulation of agricultural cooperatives. Lobbyists for cooperatives have argued that the FTC has no authority to regulate cooperatives such as Sunkist.