Secretary of State George P. Shultz moved quickly yesterday to combat Democratic claims and European fears that administration arms control policy is in disarray, reaffirming what he called "the president's firm dedication to pursue arms control agreements" with the Soviet Union.

In an apparent effort also to dramatize his growing involvement in arms control, Shultz made a surprise appearance at the regular State Department press briefing and--one day after President Reagan fired Eugene V. Rostow, the director of the Arms Control and Disarmament Agency--said, "we have the situation firmly under control."

But it seemed clear yesterday that the administration was facing a crucial problem of arms control credibility here and abroad, especially as to whether the White House could override, if necessary, a small but powerful group of conservative Republicans in Congress who had contributed to Rostow's ouster by blocking confirmation of ACDA aides, and who Rostow suggested do not want an arms accord with Moscow.

Sen. Paul E. Tsongas (D-Mass.) said that "if Rostow, a conservative, is not acceptable" to the administration, "it's really hard to see where we are going."

Sen. Joseph R. Biden (D-Del.) said the administration's efforts to brake the nuclear arms race "are in a shambles. Instead of seizing opportunities for serious negotiations, the president has capitulated to obstructionists who consider ideological purity more important than demonstrated competence."

Sen. Edward M. Kennedy (D-Mass.) said that "no president should permit the mission and personnel of ACDA to become political footballs in the hands of Senate extremists opposed to responsible arms control."

Even one conservative Republican, Sen. Larry Pressler (S.D.), called Rostow's firing "very regrettable" on grounds "it has dealt a near-fatal blow to Ronald Reagan's first-term attempt to achieve some agreement in arms control."

But administration officials, including several in ACDA, said it was not policy differences that caused Rostow's dismissal but dissatisfaction with his management of ACDA, his public outspokenness, his lack of success with Congress, and an operating style in general that grated on the White House.

Many observers, in and out of government, felt that because of these problems, Rostow never had much actual impact on policy.

To try to restore confidence in management, Shultz told reporters that the current assistant ACDA director, James L. George, will become the acting director until Reagan's nominee to run the agency, Kenneth L. Adelman, is confirmed by the Senate.

More important, Shultz also announced that his deputy, Kenneth Dam, henceforth would give day-to-day policy guidance to ACDA.

ACDA, created to help develop arms control policies as well as carry out negotiations, is already subject by law to the direction of the secretary of state. But Shultz, who has only been in office for seven months, has not until recently begun to involve himself in the complexities of arms control. His appearance yesterday was meant to emphasize that, despite Rostow's firing, talks with Moscow will go forward and policy has not changed.

Nevertheless, officials said morale in ACDA is very low. There is disarray and has been for a long time.

This is demonstrated by the appointment of George as acting director. George is the only one of four allotted assistant directors to have been confirmed by the Senate in the two years of the Reagan administration. The others have either been held up by various political factions or never nominated.

The same fate dogged Robert Grey, Rostow's choice to be his deputy, who was blocked by the conservatives. His nomination was eventually withdrawn by a White House that had once promised to back him.

Yesterday, by contrast, Grey's leading opponent, Sen. Jesse Helms (R-N.C.), said he was pleased by the nomination of Adelman. And it was learned that Sen. Barry Goldwater (R-Ariz.) has decided no longer to block the related nomination of Richard Burt as assistant secretary of state for European affairs. Burt is an arms control specialist that Shultz wants confirmed. Other conservatives may still try to block Burt, but Goldwater's opposition was considered most important.

Rostow was a confirmed hawk who took a tough line with Moscow on arms control but who also, together with one of his top negotiators, Paul H. Nitze, pressed the White House for as much negotiating room as possible to deal with the Soviets.

Adelman has little real experience in arms control, and therefore it will probably be some time before he has any impact on policy.

His new deputy, former Maine Republican congressman David F. Emery, has no experience, and his nomination has caused some concern among career officials.

Their inexperience has thrust Nitze, 75, even more into the spotlight as the central figure. He has a long history in arms control and heads the U.S. delegation to the Geneva talks with Moscow on reducing intermediate-range nuclear missiles based in Europe.

That is considered the key negotiation, because the situation in Europe will come to a head later this year when the United States is scheduled to begin deploying 572 new missiles if there is no agreement with Moscow beforehand.

The missiles are meant to counter some 600 Soviet missiles already in place. Reagan has proposed a "zero-option" plan in which the Soviets would dismantle their missiles and the West would forgo the new deployment. The deployments, however, are extremely controversial in Europe.

Nitze has been pressing for authority to explore with the Soviets some compromise solution. The arms talks are to resume Jan. 27 and Nitze will get his final instructions from the president before he leaves for Europe on Jan. 23.

Although Nitze was close to Rostow, it is known that he does not intend to resign and is willing to carry out whatever instructions he gets from Reagan. Officials acknowledged that his departure now could mortally wound U.S. credibility among the Atlantic allies, especially as to whether the administration is sincere in seeking agreement with Moscow.

Nitze is said to be confident that he will get some flexibility to discuss compromise with the Soviets at Geneva. But that is not what top White House officials are saying. They said Reagan wants to stick to his "zero-option" plan and have Nitze mostly listen for Soviet proposals that will go beyond what Moscow has already offered.

In a farewell address yesterday at the State Department to 170 ACDA employes, Rostow warned that the United States is in danger of being wrongly perceived as the country standing in the way of arms control.

"If it is not obvious" to Americans and allies abroad, Rostow said, "that the absence of agreement is the fault of the Soviets and not of the United States . . . it will be impossible to achieve worthwhile agreements with the Soviets and our alliance systems will be in grave peril."

Rostow, 69, still recuperating from a hip injury, appeared on crutches before the group and drew two standing ovations.