Labor Secretary Raymond J. Donovan, discussing a potential solution to the 19-day strike by air traffic controllers, became embroiled yesterday in a bit of a dispute himself.

At a news conference after a speaking engagement in Biloxi, Miss., Donovan said the administration was considering an offer to the controllers that would include a new "grace period" during which their dismissals could be appealed, perhaps allowing some to return to work.

President Reagan, citing the controllers' strike as illegal, had initiated a dismissal process that includes a seven-day appeal period after receipt of a dismissal notice.

Donovan said, "Could there be another such period? And I'm speaking as Ray Donovan, not secretary of labor, that's possible."

As the Professional Air Traffic Controllers Organization warmed to Donovan's remarks, claims that Donovan had been misinterpreted were issued by White House deputy press secretary Larry Speakes, Transportation Secretary Drew Lewis and Donovan himself.

"The statements by Secretary Donovan were obviously misinterpreted," Speakes said in Los Angeles, where Reagan has been meeting key advisers and members of Congress this week. "I've spoken to the president, Donovan and Lewis, and the administration position remains unchanged."

"We are not going to take them [the controllers] back," Lewis said in an interview with a Philadelphia television station.

Donovan's own spokesman clarified the secretary's remarks. "There is absolutely no validity to the report that Secretary Donovan has offered a new proposal," press Secretary Earl G. Cox said.

"Quite obviously, the secretary's remarks were taken out of context or misinterpreted. What the secretary did say, and the bottom line to it, is that he fully supports the president in the position he has taken," Cox said.

Donovan's forum was a meeting of the Associated General Contractors of Mississippi at the Broadwater Beach Hotel in Biloxi.

"All I can tell you is there is thinking, deep thinking, deep discussion," Donovan said, "trying to find a way out of what I can only describe as the most difficult legal situation as it applies to government-union relationships that anyone can remember."

Donovan's remarks were taped by WLOX-TV in Biloxi.

Donovan said he was disappointed that more of the 11,045 dismissed controllers did not appeal their firings during the seven-day grace period. Only about 130 have done so, the Transportation Department siad.

"No one is gloating over this situation," Donovan said, according to the tape. "It is not a union-busting device. That I emphatically assure you.

"The president's hand was forced. He acted as a true chief executive that he is. Now we have to find ways, if they are out there, to help ameliorate what is a tragic situation for so many families."

Donovan's remark about consideration of an additional grace period was praised by PATCO spokesman David Trick.

Trick told United Press International that Donovan's comments were "the first public indication that the administration has done anything other than issue an order to take no hostages.

"You know, 'shoot the wounded' has been their line up to now, and I consider this a mellowing of an irretractable position," Trick told UPI.

"He's a very sensitive person, and he spoke as Ray Donovan, the person, the man, not the secretary of labor," spokesman Cox said. "He made that point clear. So he does not have any inside informtion whatsoever." m

Meanwhile, in Amsterdam, the executive board of the worldwide federation of air traffic controllers met to plan a weekend conference expected to produce calls for boycotts supporting the U.S. strikers.

Portuguese controllers, who staged a boycot Monday and Tuesday of flights to and from the United States, said they would ask the federation to boycott all U.S. flights.

The Portuguese controllers had taken their 48-hour action despite an IFATCA board appeal to members to postpone disruptive actions until the weekend meeting. Some Canadian controllers had boycotted U.S. flights earlier, creating a major snarl in transatlantic air traffic before they returned to work.