The Carter administration, in its first public statement on the Federal Trade Commission's antitrust investigation of the cereal industry, yesterday said it opposes action by the agency ordering the nation's largest cereal manufacturers to split up their operations.

The statement, contained in a paper released during a visit by Vice President Walter Mondale to Battle Creek, Mich., comes less than a week after Republican presidential candidate Ronald Reagan told Kellogg Co. the FTC's landmark antitrust case against the nation's three largest cereal companies is without merit.

Mondale said that, "after eight years" of FTC study of the cereals industry, "it is inconceivable to me and to many independent experts that divestiture would be pursued. Neither President Carter nor I would support such action."

Mondale went on to say that, while he does not think the case will be resolved by Congress, the administration "certainly would" support a legislative effort to prevent the commission from forcing the cereal companies to divest themselves of key subsidiaries.

The Carter administration in recent months has made much of its support for the FTC. Just yesterday, before the Mondale statement was released, White House officials chided Reagan for his position in the cereals case.

Last week, Reagan said he would support legislation to "narrow" the FTC's authority to order divestiture in antitrust cases.

"It is clear to me that the [cereal] case under consideration has very little basis in fact and that a favorable ruling on behalf of the FTC would have a chilling effect on American industry," Reagan wrote to Kellogg Co. President William E. LaMothe.

"The cereal case is but another example of a bureaucratic crusade undertaken in the premise that the bureaucrats rather than consumers can make rational choices," Reagan wrote. The nominee has also said "it was never intended" that the FTC "have the authority to order a company to divest its assets and thereby restructure an entire industry."

The Reagan statements were attacked immediately by federal antitrust experts who raised questions both about the propriety of Reagan speaking on an ongoing judicial proceeding and whether Reagan actually has studied the complex eight-year-old case. "The question is which cereals lawyer wrote the thing," said one congressional antitrust watcher.

Sen. Howard Metzenbaum (D-Ohio), chairman of the Senate antitrust subcommittee, said he was "shocked" at Reagan's "totally inappropriate interference with the adjudicative processes of the FTC.

"Gov. Reagan has obviously injected his political objectives into an otherwise proper FTC proceeding," Metzenbaum said, noting that during this year's flap over the agency's future, Republicans said it was improper to interfere with ongoing proceedings, particularly in antitrust matters.

Metzenbaum was not available for comment after the Carter administration announced its position.

FTC officials would not publicly comment on either position in the case.

At the same time, Lamothe said Kellogg Co. is "very pleased" to have Reagan "recognize the great danger associated" with the FTC's case. He made the statement before the Carter administration position was known. The exchange over the FTC case came as the two parties intensively campaigned in Battle Creek, Kellogg's home base, for Michigan's key 21 electoral votes. The cereals case, brought in April 1972 by a commission during the Nixon administration, is a vital political issue in that Michigan area, where congressional candidates, labor unions and others repeatedly have lambasted the FTC action.

The FTC's controversial cereals case is widely believed to be among the most important antitrust cases ever brought by the federal government.

Citing a variety of antitrust charges, the FTC staff recently concluded that the behavior of the cereal industry reveals a conspiracy that the staff alleges has cost American consumers at least $100 million a year in "overcharges." The staff recommended that the three companies divest themselves of key subsidiaries.