Soviet authorities last night arrested Alexander Ginzburg, one of the country's most active dissidents, and today expelled Associated Press correspondent George Krimsky in separate moves that reflected a tougher stance toward dissenters and Western journalists who frequently write about them.

Ginzburg, who has been imprisoned twice before, was picked up when he left home last night to make a telephone call and taken by KGB security police to Kaluga, southwest of Moscow. The charges against him have not been disclosed, but friends say they are likely to be serious.

Krimsky, the first American correspondent to be expelled since 1970, was accused by the Soviet Foreign Ministry of espionage activities and violating Soviet currency regulations. He and the AP had previously rejected the allegations and pointed out that Krimsky reported extensively on the Soviet dissident scene.

[The State Department acknowleged Friday that it was considered "reciprocity" against a Soviet correspondent based in the United States, because of he expulsion order against Krimsky. "Reciprocity" would mean ordering a Soviet correspondent out of the United States, Secretary of State Cyrus R. Vance "discussed this (Krimsky) matter this afternoon with Ambassador Dobrynin (Soviet Ambassador Antoliy F. Dobrynin)," a spokesman said last night.]

The actions pose a direct challenge to the Carter administration, which has said repeatedly in recent days that it would oppose repression of human-rights activists in the Soviet Union and urge greater Soviet compliance with the relevant terms of the 1975 Helsinki accord on European security.

From the Western standpoint the Helsinki document was supposed to encourage freer expression and a greater flow of information. The arrest of Ginzburg and the expulsion of Krimsky are certain to be regarded therefore as restrictive measures.

Some of the dissidents even saw a direct link between today's actions and the Carter's administration's watering down of support for Soviet Nobel Prize winner Andrei Sakharov, the outspoken dissident supporter who was told by Soviet prosecutors last week that he faces criminal charges unless he ceases his statements.

By speaking out strongly and then apparently backing away from its initial stance after a Soviet complaint, the Carter administration has shown that it can be easily pressured, the dissidents said in an emotional press conference today.

"President Carter has betrayed us," Valentin Turchin, head of the Moscow chapter of Amnesty International said.

The U.S. embassy described the Krimsky expulsion as "an unfortunate development" and it was understood that the Soviets had been told the move could have a negative impact on Soviet-American relations. Western diplomatic sources said the combined actions of recent days were likely to have repercussions in Washington.

The mystery, as a senior Western diplomat put it, "is why the Soviets are prepared to risk that at this time."

Ginzburg, 40, who recently has administered a fund for jailed political activists and their families our of royalties from the books of exiled novelist Alexander Solzehenitsyn, is the most prominent dissident to be arrested in some time. His 1968 trial for anti-Soviet agitation was among the more celebrated of that period and after his release in 1972 he served as a secretary of Solzhenitsyn.

He has also been an assistant to Andrei Sakharov, the dissident physicist and Nobel Peace Prize winner, and was an active member of a group set up last spring to monitor Kremlin comliance with the Helsinki accords. Few other people in the Soviet human-rights movement have been as active as Ginzburg over so long a period of time.

Krimsky, 35, has been in the AP Moscow bureau since 1974. Although he covered the full range of news in the Soviet Union, Krimsky, who speaks Russian, developed wide and close contacts among the dissident community.

Last spring the Soviet weekly literary Gazette accused Krimsky and two other American correspondents - Christopher Wren of the New York Times and Alfred Friendly Jr., then of Newsweek - of being spies, charges all three denied. Subsequently, official Soviet let it be known that the allegations were merely meant as retaliation for similar charges in the American press about three Soviet journalists.

Then, on Jan. 24, AP bureau chief David Mason was abruptly summoned to the Foreign Ministry and told that Krimsky should be withdrawn. Aside from reviving the espionage charge, the Soviets said Krimsky had given hard-currency coupons used in special stores for foreigners and selected Russian stores to unauthorized Soviet citizens.

When AP refused to recall Krimsky based on what it termed such "filmsy" allegations, the Soviets acted. Mason was called in today as was U.S. embassy political counselor William Brown and told by a second-level official of the Foreign Ministry press department that Krimsky has a week "to leave the territory of the U.S.S.R."

[AP President and General Manager Keith Fuller said in New York that Krimsky's expulsion is "a flat grant violation of the Helsinki agreement as it pertains to news reporters carrying out their mission. From the facts before me I can discern only that his sin was to be an aggressive reporter in the Soviet Union today where the rising voices of Soviet dissidents seem to be unnerving those responsible for this expulsion."]

The Soviets have sought in advance to deflect Western criticism by asserting that both cases involve individuals who have violated Soviet law.

A commentary by Tass, the Soviet news agency, for distribution abroad, said tonight that a search of Ginzburg's apartment several weeks ago had turned up "anti-Soviet leaflets? as well as "large sums" of foreign currency - both of which could form the basis of criminal charges.

The allegations against Krimsky, the Soviet assert, place him outside the protection of the Helsinki accord's provision against expulsion of journalists for "legally" carrying out their professional activities.

Wren is still here as the New York Times bureau chief: Friendly left Moscow in July at the end of a two-year tour. Other Western correspondents have been attacked in the press in recent months and several have been called to the Foreign Ministry. The criticism in most of these instances was confined to the correspondent's written work.

The move against Ginzburg is also not an isolated incident. The number of searches, officials warnings to dissidents and threatening telephone calls has been increasing. Friends of Yuri Orlov, leader of the Soviet committee that has been monitoring Helsinki compliance, said his arrest is expected imminently. They said he has left Moscow.

Part of the alarm expressed today on Ginzburg's behalf was the fact that he is still weak from the effects of serious pneumonia and signs of tuberculosis. He was hospitalized until a week ago but left before recovering.