The Democratic and Republican national committees yesterday announced the dates of four jointly sponsored presidential debates and said 15 candidates from both parties have agreed to participate if nominated.

Debates sponsored by the parties would be a new element in the 1988 campaign. The League of Women Voters has sponsored presidential debates since 1976, and league President Nancy M. Neuman says it has "just as firm a commitment" from the candidates for its 12 scheduled debates next year.

"It's premature for the parties to say they have it all nailed down," Neuman said in a telephone interview. "When the candidates boil it down, they'll participate in ours."

The dates announced by the party chairmen at a news conference yesterday are Sept. 14, Sept. 25, Oct. 11 and Oct. 27, 1988. Three will match the presidential candidates, and the vice-presidential contenders will meet in one.

The league, meanwhile, is planning four debates for each party's candidates during the primary season early next year and four -- three presidential and one vice-presidential -- next fall, Neuman said. The league selected New Hampshire and Tennessee as sites for its first two primary debates.

Democratic National Committee Chairman Paul G. Kirk Jr. -- cochairman of the Commission on Presidential Debates, the bipartisan committee planning the debates -- said the political parties are not trying to put the league "out of the debate business" but are assuming their proper role in presidential elections by educating the public.

"I have applauded the league for having filled a void in the past," he said. "It's like a little boy whose older sister may have done his homework for him for some time. . . . At some point, we've got to take up our own responsibilities."

Commission cochairman Frank J. Fahrenkopf Jr., chairman of the Republican National Committee, said candidates who have agreed to participate in parties' debates are free to take part in other debates.

League officials have accused the parties of "stealing" the debates, arguing that only a nonpartisan organization can hold an unbiased debate.

The Democrats who have agreed to the parties' four dates are former Arizona governor Bruce Babbitt, Massachusetts Gov. Michael S. Dukakis, Reps. Patricia Schroeder (Colo.) and Richard A. Gephardt (Mo.), Jesse L. Jackson, and Sens. Joseph R. Biden (Del.), Paul Simon (Ill.) and Albert Gore Jr. (Tenn.)

The Republicans are Vice President Bush, Sen. Robert J. Dole (Kan.), former Delaware governor Pierre S. du Pont, former secretary of state Alexander M. Haig Jr., Rep. Jack Kemp (N.Y.), former Nevada senator Paul Laxalt and evangelist Marion G. (Pat) Robertson.