The Justice Department began a full investigation yesterday into the relationship between U.S. intelligence services and Nazi war criminal Klaus Barbie, releasing records showing that Barbie entered the United States on a Bolivian passport at least four times in 1969 and 1970.

Allan A. Ryan Jr., who is heading the inquiry, said he hopes to "compile a factual report . . . about any relationship between Barbie and the U.S. government from 1946 on, and as much as possible release it to the public."

Ryan warned that because of the statute of limitations, the investigation may not result in prosecutions, but he added that he would pursue prosecution if necessary.

Barbie, a former top Gestapo official who was known as the "Butcher of Lyons," was extradited from Bolivia to France last month to stand trial for "crimes against humanity."

Attorney General William French Smith said the Justice Department has received assurances from the CIA and the Defense and State departments that they will "cooperate fully" in the investigation.

Justice Department sources have said that Smith initially rejected the idea of an investigation because of the probability it would not lead to prosecution, but changed his mind under pressure from Congress and the White House.

Smith, questioned at a congressional hearing about his decision, denied that he had vetoed an investigation. "We had made no decision on that," he said, but added: "It is true that it is not our essential function to engage in an investigation for its historical value."

Smith said that a preliminary investigation of allegations about Barbie convinced him that a full probe was necessary. "We have seen enough to convince us that the charges that the U.S. utilized Barbie for intelligence purposes after World War II and later assisted in his escape to Bolivia cannot be dismissed and that a full investigation would be appropriate."

Ryan said the inquiry would deal with the following allegations:

* That Barbie worked with the U.S. Army's Counter-Intelligence Corps after World War II.

* That U.S. officials in Germany refused to turn him over to France for trial in 1949.

* That U.S. officials aided Barbie in obtaining travel documents when he fled to Bolivia in 1951.

Ryan added that he will look into what Barbie was doing during his 32 years in Bolivia and his four entries into the United States. Ryan is also expected to investigate published reports that Barbie may have been involved in arms smuggling.

According to the documents released yesterday, Barbie entered this country four times--in July, 1969, and January, 1970--using the name Klaus Altmann. Ryan added that it is possible that Barbie made other trips to the United States.

Ryan said that records furnished by the Immigration and Naturalization Service indicate that Barbie was using a special U.S. visa intended for officials and employes of a foreign government. The visas apparently were issued by the American Embassy in La Paz on July 17, 1969.

In information supplied for the visas, Barbie said he was born in Berlin on Oct. 25, 1915, and that he was planning to visit New Orleans, San Francisco and Miami. One of the documents shows his temporary address as they Ayers Steamship Co. in New Orleans. In an ABC News interview, company president William Ayers said that Barbie had hired his company to haul cargo between U.S. ports and South America.