The FBI has won approval from the Senate Judiciary Committee to begin modernizing its computerized criminal files, but only after it agreed to limit transmission of controversial criminal history data, it was learned yesterday.

Acquisition of an electronic communications controller will allow the FBI to significantly reduce the amount of time that it is out of contact with other police computer systems during the frequent periods that its main computer is out of order.

In a letter sent yesterday to FBI Director William H. Webster, Sen. Edward M. Kennedy (D-Mass.), chairman of the Judiciary Committee, and Sen. Strom Thurmond (R.S.C.), the panel's ranking minority member, said that "commitment to individual rights" had caused the committee to delay any modification of the FBI'S National Crime Information Center equipment.

FBI assurances "that it would take the necessary precautions to protect those rights" now makes it possible to approve the new equipment, Kennedy and Thurmond said in the letter, a copy of which was obtained by The Los Angeles Times.

Under the conditions to which the FBI agreed, the $500,000 equipment will be leased, not purchased. It will not be used for "message switching," the exchanging of computerized criminal-justice data from one state to another. And the equipment will be programmed to give "the very lowest priority" to requests for computerized criminal history information, which includes narrative responses to questions on where and when a person was arrested, the charges, and their disposition.

Critics of the Crime Information Center system have contended that some criminal history information is inaccurate and that there is a lack of uniformity among the states that utilize the system.

To insure compliance with its commitments, the FBI agreed to permit Congress' General Accounting Office to audit the system twice a year.