Disagreements between the Carter and Reagan campaigns yesterday raised doubts about whether the presidential debates will take place as envisioned by the League of Women Voters.

The president wants the first debate soon and wants it to be a head-to-head counter with Ronald Reagan, Carter campaign chairman Robert S. Struss said yesterday, Carter accepted an invitation from the National Press Club for a head-on debate early next month with Reagan; the Reagan camp said it had received the invitation but had not decided on a reply.

Reagan wants the first debate to take place later in the campaign and favors holding it under the criteria established by the league, which would permit independent candidate John B. Anderson to participate if he has at least 15 percent support in the polls on Sept. 10. Reagan also wants a head-to-head debate with Carter to come second.

The first debate is the focus of the deadlock because both campaign camps consider it by far the most important. It is almost certain to capture the largest television audience and set a pattern of sorts for any subsequent encounters among the presidential candidates.

James Baker, senior advisor to the Reagan campaign, mentioned another reason the initial debate is being highlighted. "It's terribly important to John Anderson," he said.

Anderson draws more support away from Carter than from Reagan, and a strong debate showing could boost Anderson's declining fortunes.

Strauss and Baker spoke to reporters after meeting for more than two hours in the national headquarters of the League of Women Voters here.

Each expressed confidence that debates would take place, but despite protestations that their discussions yesterday were friendly and helpful, it appeared that the two sides were no closer together when they finished than when they began.

"It took three or four meetings to get things [for the debates] worked out in 1976," Strauss noted.

On one major point it appeared that the two sides had been talking past each other.

Strauss and presidential press secretary Jody Powell said they had been unable to get an assurance that at least one of the debates would be between only Carter and Reagan.

Baker expressed surprise when that statement was repeated to him. "If we haven't given them that, we give it to them right now," he said. Reagan is on the record favoring a head-to-head debate as well as one including any other candidates who meet the league criteria.

It is the Carter forces' preference and "almost insistence," Strauss said, that a head-to-head debate be the first encounter. Baker was adamant that Reagan will not agree to any debate in advance of the first league-sponsored debate, which is scheduled for Sept. 18 in Baltimore.

Carter sought to embarrass Reagan into an earlier head-to-head meeting by accepting the invitation from the National Press Club. Powell announced yesterday that the president hopes Reagan will also accept the invitation and that the debate can be held as soon as possible.

Reagan wants the date of the initial league debate pushed back a few days because he has an important fund-raiser in Texas on Sept. 16 and wants more time to travel to Baltimore, to prepare himself and to rest before the debate. The league said it has no objection to a change of date.

Carter would like the first debate to be moved ahead to the second week of September.

The two major candidates also disagree over how many debates should be held.

Baker said Reagan wants two presidential debates and one vice presidential debate. He held out the possiblity that if negotiations remain difficult, there might be only one presidential debate.

Strauss said Carter wants as many debates as possible, under the league's sponsorship or that of others, and wants them held in all regions of the nation.

Baker said that his side doesn't want more than two debates because "then we'd spend the entire campaign debating." He said that as the challenger Reagan needs time to hold his own campaign events around the country.

In the first 16 days of September following the formal kick-off of the Reagan campaign, the challenger's schedule calls for him to spend eight days in Washington; five of them are days off.

Carter officials expressed concern that Reagan was dragging out the planning discussions in order to make sure there would be time only for one or two debates.

The league, which organized the 1976 presidential debates, announced a series of three presidential debates -- in Baltimore, Cleveland and Portland, Ore., and one vice presidential debate, in Louisville.

Ruth Hinerfield, head of the league's Education Fund, said she will call a board of directors meeting as soon as possible to discuss the problems raised at today's meeting.

She said the league could change its debate rules so that Anderson, should he qualify, would take part in the first debate, but not in a second.

The board will also discuss the number of debates, timing, and format, she said.

Anderson expressed outrage at Carter's efforts to arrange a two-man debate with Reagan. Anderson accused Carter of "political arrogance" for thinking "he has a right to tell the American people . . . who they ought to listen to in a debate."

Anderson said he was disappointed that the league had not invited him to participate in the planning negotiations. The Anderson campaign manager, Mike MacLeod, said his staff would be in touch with National Press Club officials today and ask them to reconsider the club's two-man debate plans.