A Puerto Rican terrorist group claimed responsibility fro bombings yesterday outside the Justice Department's headquarters on Constitution Avenue and at three airports in the New York and Newark area.

The mid-morning blasts caused no injuries and only minor damage, according to the FBI and other authorities. Anonymous callers also warned that bombs would go off at the O'Hare Hilton Hotel, near Chicago's O'Hare International Airport, but no explosion occured.

In Washington, the explosion took place at about 9:40 a.m. near the Constitution Avenue entrance to Justice Department headquarters, midway between Ninth and 10th Streets. Authorities said that the blast was caused by a pipe bomb that was detonated by a timing device. The bomb had been left amid shrubbery just east of the entrance, they said.

About 35 minutes later, a militant Puerto Rican independence group known as the FALN claimed it had planted bombs in several cities. Its most detailed message was given in a telephone call to United Press International in New York.

"This is FALN," a woman with a slight Spanish accent told a UPI telephone operator. "Listen carefully. We take full responsibility for actions in Newark, New York, Chicago and Washington and corresponding airports today." Catherine Downing, the UPI operator, said the caller added a partly indistinct statement indicating that a communique would be left in a "park in front of City Hall." Then the caller hung up.

An FBI spokesman in New York said later that no communique had been found. Two similarly worded messages were received at about the same time by a telephone operator at the O'Hare Hilton, according to Chicago police. These warned of bombs at the Hilton, but did not mention threatened explosions in any other city, police said.

The FALN - whose initials stand for its Spanish name which is usually translated as the National Liberation Armed Forces - repeatedly has resorted to terrorist bombings to dramatize its demands for an end to what it has termed "Yankee imperialism" in the Caribbean and the release of imprisoned Puerto Rican nationalists.

Since 1974, according to FBI officials, the FALN has claimed responsibility for about 75 bombings, including a 1975 explosion at New York's historic Fraunces Tavern that left four persons dead and 55 injured. The FALN bombings are under investigation by a federal grand jury in New York.

FBI officials tentatively linked the explosions in Washington and elsewhere yesterday to the FALN, though they said they could not be certain. The FALN message, they noted, did not specifically mention the Justice Department blast, and the explosive device set off here differed from those in New York and Newark.

Authorities said the bombs planted at the New York and Newark airports were incendiary devices, detonated by timing mechanisms composed of watches and batteies. Because of the FALN message, a search was also conducted yesterday at National and Dulles International airports here, but officials said no bomb was found.

In Washington yesterday, Robert Grooms, a Civil Service Commission investigator, was on his way to Justice headquarters when the explosion occurred. He said in an interview later that he had crouched behind his parked car after hearing what he described as a "loud, hollow sound."

"There was a large cloud of white smoke that emanated from the [Justice Department's] entrance area and completely engulfed the whole building," Grooms said. "There was plenty of flying metal. In fact, you could hear flying metal hit the trees or hit the shrubbery."

D.C. police put out a "lookout" for one possible suspect - a man in a green shirt whom Grooms saw walking from the entrance area at the time of the blast.

At the New York and Newark airports, incendiary bombs went off at about 10 a.m., causing small fires but little damage, according to Ed Franzetti, a spokesman for the Port Authority of New York and New Jersey.