he future of Argentina's fragile new Army-led government appeared today to hinge in part on the ability of president-designate Reynaldo Bignone to win the backing of civilian political leaders who are demanding a quick return to democratic government and a reversal of the military's conservative economic policies.

Leaders of Argentina's major political parties agreed last night after considerable debate to meet this evening with Bignone, a retired general whose designation as president led the Argentine Navy and Air Force to withdraw Tuesday from the six-year-old military government.

After the four-hour meeting, party leaders said Bignone had promised to lift the military government's 6-year-old ban on political activity when he takes office July 1, United Press International reported. "He left a good impression," said Carlos Contin, president of the moderate Radical Party. The formal ban on political activity has been in effect since 1976.

Bignone had said earlier that an accord with political leaders was his "first priority." The general and Army Commander in Chief Cristino Nicolaides have promised to establish a transition government that would reestablish democratic institutions in Argentina in 1984 with policies mutually agreed on by civilian and Army leaders.

In addition to Navy and Air Force opposition to Bignone's assumption of the presidency, several Army generals are reported to be dissatisfied with the new leadership of Nicolaides in a continuing military power struggle following Argentina's defeat in the Falkland Islands.

During the past several days, the dissension within the military has been heightened by the appearance of new details about Argentina's military effort against Britain on the Falklands. Returning soldiers were quoted today as saying they were scantily trained and poorly equipped and fed.

Political leaders and government sources said today that if civilian leaders refused to back Bignone, he would be dealt a crippling blow that could plunge Argentina into a new round of political chaos.

"This is the weakest government the country has had in many years," said Francisco Manrique, the leader of the right-wing Federalist Party, who joined more than a dozen other politicians in the meeting with Bignone at the Argentine National Congress building. "The only support that Bignone has now are the political forces. If they refuse to meet with him, he is finished."

Political analysts here noted that the crisis within the Argentine military following the humiliating surrender to Britain last week had given the country's political leaders substantial negotiating power with the armed forces for the first time since the military ousted the civilian government of Isabel Peron in a March 1976 coup.

Several of the politicians were eager to agree with Bignone on a government plan and to avoid further political crisis, political sources said. But Bignone and Nicolaides, who are to replace Gen. Leopoldo Galtieri in his posts of president and Army commander in chief, were believed to hold conservative political views unacceptable to the parties.

Political leaders, including the five largest political parties acting as a front, demanded that the Army organize elections to restore democratic government as early as six months from now and replace the armed forces-backed free-market economic policy with a government-sponsored campaign to stimulate Argentine industry and jolt the nation out of its severe recession.

In a policy document issued last night, the multiparty front, which includes the Peronist and Radical parties, also called for Argentina to shift its foreign policy away from identification with the United States to a clear nonaligned position. The document strongly attacked the joint military government that ruled Argentina until this week as having led the country into "the most grave crisis in its history as an organized nation."

The political leaders' position is supported to a large extent by leaders of the Air Force and Navy, who were prompted by the Falklands conflict to drastically reshape their views of Argentina's foreign and domestic policies. These forces urged the Army to accept a civilian as president and abandon the military's past political plans before abandoning the government.

In contrast, the current leadership of the Army is described by military and political sources as an essentially conservative movement seeking to prevent the Falklands crisis from bringing about drastic changes in Argentine politics.

Nicolaides and the top 10 Army division generals who installed him in power are said to favor a continued alliance with the United States, a slow transition to democracy similar to that already planned by the military and a quick settlement of the military conflict with Britain in favor of diplomatic negotiations.

Political sources questioned, however, whether the ruling generals could continue to maintain their position amid continuing turmoil and recriminations over the timing, planning and execution of the April 2 Falklands invasion and its disastrous end 74 days later.