As the outgoing Carter administration kept a wary vigil through yet another day of the hostage crisis, the incoming administration announced the formation of a task force to assure continuity of negotiations, should the hostage release not be completed before President-elect Ronald Reagan is sworn in at noon today.

Reagan's press secretary, James S. Brady, announced that the president-elect has ordered formation of an interagency task force on the hostage issue, including members from the outgoing Carter administration, so that "at 12:01 p.m. tomorrow [Tuesday] the people who have been working on this won't suddenly be gone." The task force will include representatives of the State, Defense, Justice and Treasury departments as well as members of the National Security Council and White House counsel's office.

White House press secretary Jody Powell said yesterday that if the Carter administration leaves office without all facets of the deal with Iran being completed, there will be "no obligation" on the part of the next administration to carry it through.On the other hand, Powell said, "an agreement that has been completed and has brought our people back would be honored by an incoming administration."

Meanwhile, Carter and members of his outgoing administration, who began the day in the early-morning hours with champagne and elation, became increasingly cautious as the release of the American hostages in Iran was postponed.

As of early evening, senior State Department officials said they could not predict whether departure of the 52 captive Americans from Tehran would come within a matter of a few hours, or whether more serious complications are involved.

Carter, who had hoped to fly from Washington to Wiesbaden, West Germany, to greet the hostages, was forced to cancel the presidential trip he wanted most to take. Air Force One was prepared for his departure at Andrews Air Force Base, the entrance ramps pulled up to the plane, and a chartered Pan American jetliner was waiting nearby for the accompanying press party when the cancellation was announced.

Powell said Carter may yet make the trip to Wiesbaden, but as a private citizen representing President Reagan According to Powell, Reagan telephoned Carter at 9:20 a.m. yesterday with a "most generous offer" to be the official U.S. representative at the hostages' arrival in Germany if the event takes place after noon today, when Reagan assumes the presidency. Carter accepted the offer in a telephone call to Reagan shortly after 2 p.m., Powell said.

Reagan said he was keeping his "fingers crossed" until all of the hostages were airborne out of Iran "in view of the history of this whole thing."

Carter announced the completion of the agreement with Iran at 4:58 a.m. yesterday in the White House press room, and planning was under way for the whirlwind presidential trip to see the hostages in Wiesbaden and to return in time to turn over the presidency to Reagan at noon today.

The euphoria lasted until late in the morning, when the first indications of a delay were received. State Department spokesman John Trattner, who declined to use the word "delay," nevertheless cautioned reporters at noon that it was "a hope more than a prediction" when hostage families were informed that their loved ones might be released yesterday.

Trattner said that in a "rather unusual situation" the United States was moving calmly and deliberately toward release of the Americans. He steadfastly declined to describe the speed of this pace, or to predict when the Americans would depart Iran.

By early afternoon, time had run out on Carter's opportunity to make the quick trip he planned. At his news conference announcing that Carter would not go to Wiesbaden, Powell expressed optimism about a hostage release before noon Tuesday, but he also spoke of the problems that would arise if the deed were delayed.

When a reporter asked if the delay in Tehran had been calculated to ensure that Carter would be unable to see the return of the captives in his term of office, Powell replied with some exasperation, "I don't have any way to look inside their heads over there."

Secretary of State Edmund S. Muskie, in a farewell talk to State Department employes in the late afternoon, confidently declared, "They will soon be free. They will soon be home. But our celebration of their release is muted by the suffering that has been so bravely endured."

After his speech, Muskie told reporters that "we're plowing our way through [the difficulties that had arisen]. I think it is manageable." He added, however, that "there are no guarantees."

Suddenly senior Carter administration officials who had expected to spend most of Monday cleaning out their desks and saying goodbyes found themselves caught up in a final Persian puzzle, one of many they have had to face in the final 14 months of the administration.

Muskie and several other senior State Department officials who had not expected to come to work on Tuesday, when they have only a halfday of official time left, had to revise their plans. The secretary of state as well as other lame-duck officials involved in the long-running Iran crisis will be at their desks until 11:59 a.m. today if the hostages are not out by then, according to official sources.