The head of the nation's largest auto company called on the Reagan administration yesterday to put aside its internal split and ask Japan to trim auto exports here voluntarily by 300,000 to 500,000 vehicles a year.

Appearing on the CBS-TV program, "Face the Nation," Roger Smith, the new chairman of General Motors Corp., said he believes the Japanese quickly would go along with such a request to avert tougher protectionist legislation later.

Smith also suggested GM might be willing to give the United Auto Workers Union a new profit-sharing program as part of its contract negotiations next year if workers would cut absenteeism and give up some paid personal holdiays.

And, he called on the Environmental Protection Agency to roll back existing limits on carbon monoxide emissions, which he charged were too stringent and costly. He promised to reduce prices by $60 a car if EPA agreed to such a move.

Smith's admonition to the administration was buttressed by Senate Democratic leader Robert C. Byrd (D.W. Va.), who told a UAW conference Reagan should "alert the Japanese" not to boost their auto export plans dramatically.

Byrd told a group of reporters Saturday that if the president does not negotiate "voluntary" limits with Japan soon, then Congress will take up import legislation, which most observers believe is apt to be more restrictive.

Reagan's advisers have been split over the auto import question, with the Transportation and Labor secretaries pushing vigorously for voluntary restrictions and the president's economic advisers opposing them.

The United States imported an estimated 1.9 million Japan autos last year, cutting sharply into GM, Ford and Chrysler sales and contributing to a record $4.2 billion loss here by domestic auto manufacturers.

Discussions within the Reagan cabinet have involved possible "voluntary" ceilings by Japan ranging from 900,000 vehicles a year to 1.8 million. Smith's figures yesterday would fall in the middle of that range.

Smith conceded yesterday his request for import talks contradicts his previous call for "getting the government out of business," but he said the industry can't bargain with Japan on its own and this would avert a trade war.

He said he thought persuading Tokyo to go along "is not going to be nearly as difficult as some would have you to believe" because the Japanese already realize it's "in their own best interests."

He said any voluntary restrictions should be "short-term" just to give U.S. automakers enough "turnaround" time to get the domestic industry back on its feet. "But I think somebody ought to ask them," he said of the Japanese.

Smith described his call for a rollback of carbon monoxide standards as "No. 1 on my list" of federal regulations he would like to see changed. He said the $60 price-cut he vowed was the cost the requirement adds to each car.

At the same time, however, Smith insisted he did not "want to take up all the regulations," saying "we have to recognize we need (some)." Partly because of time restrictions, the carbon monoxide standard was the only one he cited.

Smith's offer to grant UAW members a profit-sharing plan to return for other concessions was a reversal of the automakers' longstanding opposition to any such move.

However, he said, "this is the profit-sharing now" because the industry has low profits and "it lets the worker participate in his efforts more directly." He said previous proposals all have been "on top of" other demands.

The debate over imports was joined later by consumer advocate Ralph Nader, who proposed the UAW help dent Japanese sales here by financing an advertising campaign to convince American buyers that Tokyo's vehicles are unsafe.