The FBI has begun an investigation to determine whether the civil rights of Arab Americans were violated by recent attacks on regional offices of the American-Arab Anti-Discrimination Committee, including a suspicious fire last week at the committee's national headquarters in Northwest Washington.

The widening of the FBI's current investigation, which was ordered by the U.S. Justice Department, had been sought by former U.S. senator James G. Abourezk, national chairman of the ADC, and was announced one day before Abourezk is to meet with FBI Director William H. Webster.

Abourezk, a frequent critic of what his group views as discrimination against Arabs and Arab Americans, said yesterday that he was "very happy" about the FBI's investigation.

"It indicates to me that they are pushing this whole matter higher up on their agenda, which is exactly what we're working for," he said.

Two of the attacks against the ADC, the bombing of the group's Santa Ana, Calif., office that killed its West Coast director and an explosion that injured two police officers trying to disarm a bomb found at the group's Boston office, already were the subjects of a criminal investigation.

But the FBI has said there was nothing to indicate the fire last Friday at 1731 Connecticut Ave. NW was a terrorist attack.

The fire, which began two floors below the ADC offices, has been termed "very suspicious" in origin and is being investigated by the Treasury Department's Bureau of Alcohol, Tobacco and Firearms, the D.C. Fire Department and the D.C. Police Department's Arson Unit.

The FBI has assisted in some aspects of the investigation, a spokesman said.

Earlier this week, Abourezk turned over to the FBI what he described as "evidence" that one person may be responsible for the fire and the two bombings at the group's regional offices.

Abourezk, who is to meet this morning with Webster and Associate Attorney General D. Lowell Jensen to discuss the information, said he hopes to be able to focus the discussion on "anti-Arab racism."

"I want to impress on them that the reason the government has been ignoring these incidents, I believe, is based on anti-Arab racism. There just has been no outcry raised against this kind of terrorism. No one has gone on the Senate or House floor to condemn anti-Arab racism, the Reagan administration has said nothing, and the FBI has laid back," Abourezk said.

He said the incidents at his organization's offices are "without question designed to intimidate the ADC into silence."

John Wilson, a Justice spokesman, said that information gathered by the FBI in its criminal investigtion "will be sent to the civil rights division so they can review it from a civil rights standpoint. The agents on the street will also be looking at it from a civil rights standpoint, where perhaps they weren't before."

The civil rights division of the Justice Department monitors laws dealing with conspiracies to violate a person's civil rights and laws governing federally protected activities, such as a group's right to meet, he said.

"The civil rights division, having seen reports in the papers and on TV about these incidents, decided it is something it should be taking a look at, since it enforces those laws," Wilson said. "There was no specific request" made to Justice to initiate the investigation, he said.

Last month, an FBI spokesman said the bureau's specialists on terrorism had concluded "there is a possible link" between the militant Jewish Defense League and the bombing of the ADC's Santa Ana office on Oct. 11. The ADC's West Coast regional director, Alex Odeh, was fatally injured in the blast, which occurred when he walked through the front door of the office and apparently triggered a trip wire rigged to a bomb.

The JDL, while praising the bombing and the death of Odeh, has denied any involvement in the incident.

FBI agents also have indicated that the JDL may be linked to two bombings in New York and New Jersey that were aimed at former Nazi Party members, which along with the Santa Ana bombing have been classified as "terrorist" acts.

On Sept. 6, Tscherin Soobzokov, 67, an admitted former member of the Nazi SS, was fatally injuredwhen a bomb exploded as he stepped from his home in Paterson, N.J., to investigate a car that was on fire in his driveway, according to the FBI.

On Aug. 16, Elmars Sprogis, 70, a former Latvian police officer, had his right foot blown off by a bomb after a fire had been started against the side of his house in Brentwood, Long Island, an FBI spokesman said.

In both cases, a bomb with some sort of trip wire was rigged near the front door of the houses, the FBI said, and the fires were apparently a "ploy" to lure the victims from their homes.

The JDL had stagged a number of protests outside of Soobzokov's home in the weeks before the blast, the FBI said, and about an hour after the explosion at Sprogis' home, a local newspaper received a telephone call from a man who said: "Listen carefully. Jewish Defense League. Nazi war criminal. Bomb. Never again."

Irv Rubin, JDL national chairman, said in an interview this week that his organization had nothing to do with any of the incidents and that the FBI was "trying us in the media, and this is wrong. We cannot sue them, and they can say anything they want."

In a telephone call to two newspapers, a person claiming to be a JDL member also claimed responsibility for a bomb that was found propped against the door of a building in Boston that houses the ADC's office. Two police officers were injured when they took the bomb to a disposal sight about two hours later and it exploded while they were attempting to disarm it.

This past week, telegrams were received in the ADC headquarters here that also purportedly linked the JDL to last week's fire.

Rubin denied that the JDL was responsible for either ADC attack or had sent the telegrams, saying that the ADC "wants sympathy so badly they are even willing to set fire to their own establishment . . . . This is a set-up, and the Arabs are doing it."

The JDL is a militant organization founded in 1968 by Rabbi Meir Kahane, now a member of the Israeli Knesset. In an interview earlier this week on the Larry King radio program, Kahane, who no longer has ties to the JDL, said, "There is no question that these Arab groups are front groups for the PLO [Palestine Liberation Organization], and therefore on a moral basis I'm not going to get up and say it's [the attacks on the ADC] a bad thing. But on a practical basis, I think it's a stupid thing."

Daniel Thursz, president of b'nai b'rith International, who along with the Jewish Community Council of Greater Washington and other Jewish organizations has condemned the apparent arson fire at the ADC headquarters, said yesterday that "the JDL is condemned by most major Jewish organizations."

"They have advocated violence -- and I have no idea if they are involved in these incidents -- and they have refused to accept any community discipline."

ADC head Abourezk has said he does not believe the person responsible for the incidents is connected to the JDL.

Abourezk said that security has been beefed up at the nine ADC regional offices around the country and that he has asked police for additional patrols in the neighborhoods where the offices are located.

"We don't want a new front of the Middle East war to open up in the United States," he said. "We are absolutely convinced that this kind of terrorism is a greater threat than anything that has occurred outside the United States."