The United States acknowledged yesterday that its attempts to act as mediator in the Falkland Islands crisis remain stalled and said there is "very little basis for optimism" that Britain and Argentina can be diverted from their collision course toward war.

That gloomy view came from the White House and State Department as administration spokesmen conceded that hopes of resuming Secretary of State Alexander M. Haig Jr.'s shuttle diplomacy were fading rapidly in the face of both sides' dissatisfaction with U.S. proposals for a negotiated solution.

In identical statements, White House deputy press secretary Larry Speakes and State Department spokesman Dean Fischer said: "The situation remains very serious. There is no movement and very little basis for optimism."

Asked about the status of Haig's peace-making efforts, Fischer replied that "we remain in touch with both parties." But he added: "It is the secretary's assessment that there is little basis for optimism that a settlement can be achieved."

The admission that Haig's role as mediator might be played out came as heavy pressure mounted in Congress for the administration to abandon its evenhanded stance of the past four weeks and to side openly with Britain.

The House Foreign Affairs Committee adopted, by voice vote, a resolution saying that if the dispute is not settled peaceably, the United States should give "full diplomatic support" to Britain.

The Senate was scheduled last night to debate another resolution, cosponsored by a majority on the Foreign Relations Committee, saying the U.S. government "cannot stand neutral" in Britain's effort to achieve full withdrawal of Argentine forces that occupied the Falklands April 2.

The administration, apparently seeing the congressional restiveness as a way of signaling Argentina that widened warfare will bring the United States into Britain's corner, took what Fischer called a "hands-off policy" toward the congressional moves.

That decision reflected growing administration impatience at what is regarded as Argentine intransigence and stalling.

Although administration officials remained reluctant yesterday to choose sides publicly, it has been made clear to Argentina's military government that, in the event of a new armed conflict, the United States intends to "tilt" toward Britain and blame Argentina for rebuffing Haig's mission.

Efforts to pursue the latest U.S. proposals stopped Sunday when British forces recaptured South Georgia island and Argentina broke off efforts to negotiate with London through Haig.

Argentina still has not replied formally to the U.S. ideas and, when Fischer was asked yesterday if Washington expected a response from Buenos Aires, he said, "You will have to ask the Argentinians their intentions."

At a meeting Wednesday with Haig, Argentine Foreign Minister Nicanor Costa Mendez is understood to have said that his government rejects key aspects of the proposal but wants clarifications and more time to study them. Haig reportedly replied that no time is left.

Underlying the gloom in official circles here is the belief that it will be almost impossible to avert heavy fighting after Britain puts into effect today its broadened and air and sea blockade of the Falklands.

Key factions of the military junta controlling Argentina, including the commander of the Argentine fleet, are thought by U.S. officials to be demanding a showdown with the British armada, and defiant statements coming out of Buenos Aires yesterday appeared to make increasingly remote the likelihood that the Argentines will back down.

Although some officials privately described it as "going through the motions," the administration remained in touch with both sides yesterday. The emphasis was on trying to underscore to Argentina that Prime Minister Margaret Thatcher's government will not yield on its insistence that Argentine forces must be withdrawn from the Falklands before any negotiations about Argentina's claim to sovereignty.

"We're discussing the entire situation," Fischer said in reference to these continuing contacts.

But, in the face of persistent questioning, he kept falling back on his statement that there is "very little basis for optimism" and "no movement toward a peaceful resolution" in terms of the U.S. proposals or other possible approaches.