Attorney General Griffin B. Bell said yesterday that he believes the Supreme Court would rule unconstitutional a bill to provide tax credits to parents who pay tuition for children in religious and private elementary and secondary school.

He based the opinion on past decisions by the court that the Justice Department's Office of Legal Counsel interpreted the same way in a 10-page memo.

In the Senate, where 51 of 100 members have cosponsored tuition-credit legislation, the Finance Committee voted 14 to 1 three weeks ago to report a bill. In the House, 250 of 435 members have co-sponsored similar proposals.

Meanwhile the Carter administration has sponsored a middle-income student assistance bill, a proposal to provide aid similar to tuition tax credits at the post-high school level. This proposal would be constitutional, Bell said in a letter to the Department of Health, Education, and Welfare released by Secretary Joseph A. Califano Jr.

Sen. Daniel Patrick Moynihan (D-N.Y.), one of the sponsors of the tuition credit bill approved by Senate Finance, said that the court was "wrong" in the principal decision relied upon by Bell and Assistant Attorney General John M. Harmon, who wrote the memo.

Moynihan said that Congress should enact and the president should sign the bill to give the court a chance to reverse the decision, which it issued in New York case called Nyquist in 1973.

The decision invalidated a plan providing either limited reimbursements of tuition paid by low-income families to non-public elementary and secondary schools, or, for families with higher incomes, tuition tax credits varying with ability to pay.

The court held that the plan failed to achieve one of its primary purposes, the promotion of pluralism and diversity in education, because it aided religious education in violation of the First Amendment to the Constitution.

In the memo to Bell, Harmon said he does not believe the differences between the plan and the Senate bill are of "constitutional dimension."

Moynihan, saying the opinion need not bind Congress in any case, disagreed.The bill would make American pluralism "more secure," he said.

Another sponsor, Sen. William V. Roth (R-Del.), charged that "Bell is entitled to his opinion, even if it serves the political purposes of Carter, Califano & Co." The third principal sponsor is Sen. Bob Packwood (R-Ore.).

Califano, who requested an opinion in a Feb. 8 letter to Bell, said yesterday that he is "still pursuing every constitutional means to provide assistance to private schools in fulfillment of the president's commitment" in his election campaign to do that.

The Harmon memo was dated Thursday. On the same day, the House Rules Committee started to debate whether to report the administration's middle-income assistance bill under a rule permitting it to be amended on the floor to include the Senate bill for tuition tax credits.

On Friday, while the committee continued to consider the question, Rep. William D. Ford (D-MIch.) moved to bring up the administration's measure tomorrow under a suspension of the rules - meaning that two-thirds of those voting could adopt it without allowing it to be amended.

Ford is chairman of the House Education and Labor subcommittee on post-secondary education. He has been at the White House earlier in the day, according to an aide to Rep. Bill Frenzel (R-Minn.), a member of the tax-writing Ways and Means Committee and principal sponsor of the prososal pending in House Rules.

In a "Dear College" letter to be distributed tomorrow morning to all members of the House, Frenzel and two allies, ALbert H. Quie (Minn.), senior Republican on the Education and Labor Committee, and Lawrence Coughlin (R-Pa.), denounced the effort to suspend the rules as "a brazen plot by our leaders" to block a House vote in Tuition tax credits.

The letter urges a "no" vote against suspension of the rules, in opposition not to the substance of the bill but to "parliamentary chicanery by a few powerful members."