Sen. Edward M. Kennedy (D-Mass.) yesterday took another of what is becoming an almost daily shot at the Carter administration budget. This time his target is the proposed $110 million cut in funding for the Law Enforcement Assistance Administration.

Kennedy, who as new chairman of the Senate Judiciary Committee oversees the much-criticized LEAA, called the $536 million Carter budget request for LEAA "unwise, unnecessary and unfair."

He noted the LEAA cut amounted to nearly all of the $111 million reduction proposed for the total Justice Department budget of $4.2 billion for fiscal 1980.

Kennedy promised to try to restore the cuts and said if that wasn't possible he would try to amend the administration-backed LEAA authorization bill he introduced yesterday.

The amendments, he said in a sharply worded statement, would assure that most of the cuts would come from the new federal programs on statistics and research, not from the crime-fighting grants to the nation's states, counties and cities, as the administration budget proposes.

Kennedy said "one cannot help but wonder about the administration's future commitment" to LEAA because the agency seemed to have such a low priority.

He said federal officials "are all too eager to become conscientious budtet cutters at the expense of the only major federal criminal justice program providing financial and technical assistance to states and localities."

The senator's vehement statement yesterday contrasted sharply with the lovein he and Attorney General Griffin B. Bell held last August at a hearing. That day Bell endorsed a similar administration proposal to reform LEAA -- and increase its budget authorization to $825 million, a 25 percent jump.

Bell had come to Washington determined to abolish LEAA, which has spent $6 billion in the past decade without a noticeable effect on reducing crime, according to critics.

The attorney general admitted at last summer's session that he had to backtrack because he'd run into political reality: a coalition of congressional backers, like Kennedy, and criminal justice professionals who had mounted a successful fight against the dismantling.

"You can buy a lot of support for $6 billion," a Bell aide mused them.

Kennedy's insistence on keeping up the flow of dollars to the cities had been clear ever since aides circulated a memo more than a year ago promising other members of Congress no states would lose money under his bill.

"This is the only way politically to get congressional approval... to buy off the opposition," the memo said.

Kennedy's statement yesterday noted that he often has criticized LEAA defects and said the new bill "is desigred to deal with the problems which have plagued the agency and limited its impact."

A Kennedy aide noted later that cosponsors of the legislation included Sen. Strom Thurmond (R-S.C.), the ranking minority member, and several other members of the Judiciary Committee. Rep. Peter Rodino (D-N.J.) is expected to introduce the same bill in the House.

Bell's spokesman, Terry Adamson, issued a statement yesterday that commended Kennedy for introducing the bill and tiptoed around the dispute over the budget requests.

"While there may be some differences of opinion about the level of future authorizations, there is general agreement that the bill will result in greater benefits from the public's tax dollars," he said.