That group, the American Israeli Public Affairs Committee (AIPAC) allegedly passed the secret information to the Israeli government.
The suspect has not been named, but the quoted officials say the analyst works for the office of Douglas J. Feith, the undersecretary of defense for policy at the Pentagon. Feith is an influential aide to U.S. Defense Secretary Donald Rumsfeld.
The Pentagon released a statement saying the FBI investigation involves an employee who works at "the desk officer level." The Pentagon says that employee was not in the position to have significant influence over U.S. policy.
The Pentagon says it is cooperating with the U.S. Justice Department on the case.
One of the quoted officials who revealed the probe to Western media said the person under investigation had access to sensitive information about U.S. policy on Iran.
A spokesman for the Israeli Embassy in Washington, David Seigel, has called the allegations "completely false and outrageous."
AIPAC also denies the charge.
Yuval Steinitz, a member of the Israeli Parliament and chairman of Israel's Foreign Affairs and Defense Committee, says he is confident there is no Israeli espionage being conducted against the U.S. government.
"I can tell you with confidence that Israel is not spying in the United States or in the Pentagon -- period. Since the Pollard case 20 years ago there was a clear and firm decision not to spy against the United States government or in the United States and therefore I am 100 percent confident that there is no Israeli involvement in this case," Steinitz said.
Steinitz also said he is confident that U.S. officials will confirm that the allegation is false.
"I have a lot of confidence in the United States investigation authorities and therefore I am completely confident that in the end of the day it will be confirmed that there is no Israeli involvement in such a case," Steinitz said.
Yesterday, AIPAC released a statement saying that any allegations of criminal conduct by AIPAC or its employees is "false and baseless." The statement also says that AIPAC is fully cooperating with U.S. investigating authorities.
It's not the first time that Israel has been accused of spying on Washington.
One of the most damaging blows to U.S.-Israeli relations in recent history came in the mid-1980s, when Israel was caught in an espionage scandal involving Jonathan Pollard, a U.S. Navy intelligence analyst. Pollard was later sentenced to life in prison.