Britain sent detailed, written proposals for settling the Falkland Islands crisis to Washington today as Foreign Secretary Francis Pym told Parliament he hoped to make progress toward a peaceful solution in talks beginning Thursday with U.S. Secretary of State Alexander M. Haig Jr.

While refusing to express any optimism about a settlement, a senior British source noted that once a summary of the new British negotiating position reaches Washington today, there will be written proposals on the table from both Britain and Argentina for the first time. "We are now at the beginning of real negotiations," this source said.

Pym warned, however, that achieving a settlement was "not in any way going to be easy." With the vanguard of Britain's powerful naval task force now believed to be less than a week from the vicinity of the Falklands, Pym told members of Parliament they "have to face" the possibility that military means may still be necessary to force Argentina's withdrawal.

Argentina announced today that Foreign Minister Nicanor Costa Mendez also would travel to the United States this weekend and indicated that he would conduct further talks with Haig, Washington Post correspondent Jackson Diehl reported from Buenos Aires.

The official purpose of Costa Mendez's visit is to present Argentina's position to Monday's special meeting of the Organization of American States. Argentine officials indicated that a decision on whether Costa Mendez would meet with Pym had not yet been made.

American officials involved in seeking a peaceful solution to the crisis said Wednesday that they viewed the relatively moderate tone of recent British statements as a cause for optimism.

But the same sources expressed concern over who is really in charge in Buenos Aires. Sources said there seems to be a degree of distrust among the various members of the Argentine military junta, some of whom apparently see themselves as possible successors to President Leopoldo Galtieri.

Assistant Secretary of State Thomas O. Enders told the House Subcommittee on Latin American Affairs, "Time is running out on this crisis . . . . There is a danger of further military action, and we are at the most critical point."

At one point in his address to Parliament today, Pym appeared to rule out using force "so long as negotiations are in play." But he later returned to the crowded House of Commons chamber to make an unusual statement correcting himself, saying "however hard I was trying to achieve a peaceful settlement, the use of force could not at any stage be ruled out."

An aide said Pym had made "an unfortunate slip of the tongue." Several members of Parliament said they would be surprised if Britain initiated hostilities while negotiations continued, although the government must still threaten military action to keep the pressure on.

Although Pym refused to reveal any details of the new proposals he will discuss in Washington, he said, "Any negotiation which is concluded satisfactorily must deal with certain critical points, in particular, arrangement for an Argentine withdrawal, the nature of any interim administration of the islands, and the framework for the negotiations of the long-term solution."

He said the new Argentine proposals "still fail to satisfy our essential requirements in certain important respects relating to these points. They reflect continuing efforts by Argentina to establish by her aggression and her defiance of the United Nations--a defiance continued and aggravated by her reinforcement of her invasion force--what could not be established by peaceful means."

But, referring to one point of contention--the question of who would administer the Falklands following an Argentine military withdrawal while future sovereignty is negotiated--Pym said, "I would not exclude any possibility at this stage."

Members of Parliament and commentators interpreted this remark as movement away from earlier Thatcher government insistence on the restoration of unfettered British administration before sovereignty negotiations could begin. Nicholas Winterton, one of a number of right-wing members of Thatcher's Conservative Party in Parliament who strongly oppose anything other than a total return to British sovereignty and administration of the Falklands, said he is "worried about what Mr. Pym is going to Washington to do."

Other Conservative backbenchers who favor avoiding war by reaching an acceptable compromise settlement said they believed Pym's intention was to seek some form of shared British and Argentine interim administration of the Falklands. But they questioned how much Thatcher was willing to compromise or whether she was ready to alienate the right-wing Conservatives who have been her power base.

One Conservative said Thatcher has concentrated on military preparations at recent Cabinet meetings and has not indicated to the full Cabinet how far she is prepared to go to achieve a negotiated settlement. This source said some Cabinet members believed it was necessary to emphasize to the prime minister their strong desire to exhaust all possibilities for a peaceful settlement.

A Conservative lawmaker said he believed that Pym, who became foreign secretary after the resignation of Lord Carrington at the beginning of the Falklands crisis, is "in a strong position" to greatly influence Thatcher. "She can't afford to lose two foreign secretaries, and Pym has a good understanding of the Conservative Party," he said.

At a packed private meeting of Conservative members of Parliament last night, Pym stressed his determination to seek a diplomatic settlement while saying he would not "flinch" from military action if necessary. Right-wingers said later he appeared firm about British insistence on a complete Argentine military pullout and the right of the 1,800 English-speaking Falklanders 1,800 to have a say in their future.

But other participants noted that Pym deflected questions about Argentine participation in an interim administration and about reconciliation of the islanders' right to self-determination with Argentine insistence on assurances that talks will satisfy their sovereignty claim.

A number of Conservatives at the meeting continued to insist on unconditional Argentine withdrawal, participants said, and two threatened to refuse to adhere to party discipline in Parliament if Thatcher's government settled for less.

But when one legislator argued that it would be bad for military morale if the task force returned to Britain without at least seizing South Georgia Island, Pym told him it would be best for morale if the task force--like the troops of the "Grand Old Duke of York" in a well-known English nursery rhyme--forced a diplomatic settlement and returned without firing a shot.

Washington Post staff writer Michael Getler reported the following from Washington:

U.S. sources believe the main chance to avoid a military confrontation is to find some kind of solution that allows both sides to save face.

Despite continuing reports of the approach of the British fleet to the region around the Falklands, informed sources here say there still are only "a couple of ships" south of Ascension Island in the mid-South Atlantic and that the bulk of the British armada is still 3,000 to 3,500 miles and a week or more away.

Some specialists here believe that the Argentine fleet probably could penetrate the proclaimed British war zone around the islands because the British only have a few submarines in the region while Argentina would have support from its Air Force. But the relative quiet of the Argentine Navy thus far is viewed as a hopeful sign here.