CHAPEL HILL, N.C., SEPT. 11 -- Nine presidential candidates debated education issues in two separate forums here today, with Democrats all calling for increases in federal funding and Republicans sparring over whether the federal government should provide parents with vouchers that would permit them to send their children to the public, private or religious schools of their choice.

The most unconventional proposal was put forth by former Delaware governor Pierre S. (Pete) du Pont IV (R), whose "universal choice system" would give parents a voucher they could redeem either at a local public school or at a private school, where they would get a credit equal to the average expenditure per pupil in their home district.

Rep. Jack Kemp (R-N.Y.) said such a plan could undermine public education and cost up to $25 billion a year. He said he favors offering parents a choice among nearby public schools and providing them with tuition tax credits for private elementary and secondary education.

The back-to-back discussions, sponsored by the University of North Carolina, drew seven Democratic candidates but only two Republicans, prompting the moderator of the Democratic session, former North Carolina governor James B. Hunt (D), to inject a partisan dig, saying that the disparity showed "something about the differences between the two parties."

His remarks set a tone for the 90-minute Democratic forum, as the candidates disagreed with the Reagan administration's cuts in education funding while they agreed with each other on support for merit pay for teachers, increased funding for early childhood programs, college loans and grants and AIDS education, and opposition to tuition tax credits.

Their target of choice was Education Secretary William J. Bennett, who gave two speeches leading up to this event, including one here the night before the debates, warning presidential candidates not to pander to the National Education Association, which he called the nation's "most entrenched and aggressive opponent of education reform."

"William Bennett is on a witch hunt against the NEA. And he ought to be fired right now," said Bruce Babbitt (D), a former Arizona governor. "I see Al Shanker {head of the American Federation of Teachers}, in the audience, and I'd a lot rather have him as secretary of education."

"I think the secretary's effort to make opposition to the NEA and AFT a litmus test for intestinal fortitute is absurd," said Massachusetts Gov. Michael S. Dukakis (D). "If you can't work with teachers, you don't deserve to be president."

Sen. Albert Gore Jr. (D-Tenn.) said of his "top priority" in education: "On election night, I'd send a telegram to William Bennett and tell him to clear out his desk. I'd appoint a working teacher as secretary of education." Gore bumped into Bennett afterward; the secretary refused to shake his hand.

"I wouldn't take any of their calls," said Bennett, who appeared to delight in his role as lightning rod. He called the Democrats' performance "boring" and said of their response to his warning: "El foldo."

Bennett has been a leading advocate of merit pay for teachers, a concept the NEA generally opposes and the AFT -- second to the NEA in the number of teachers it represents -- generally supports.

The Democrats on today's panel endorsed the idea in principle, though without much detailed exposition, and also with calls that the base level of pay for all teachers should be raised. (They acknowledged this is a state and local issue but said the president should use his "bully pulpit.")

Rep. Richard A. Gephardt (D-Mo.) said the federal government, before encouraging merit pay, needs first to fund more research on the best methods of teacher evaluation. Babbitt said he thinks accepted standards already exist and proposed moving quickly.

Jesse L. Jackson (D) took a slightly different tack from the others, arguing that extra pay should go to teachers in "war zones," inner-city neighborhoods where teaching conditions are most difficult.

Keith Geiger, vice president of the NEA, said afterward that all the Democratic candidates "sounded good" and that it will be "very difficult" for the 1.8 million-member union to choose a candidate when it meets in December to consider an endorsement.

The Democrats all opposed tuition tax credits. Sen. Joseph R. Biden Jr. (D-Del.) surprised Hunt when he said he had never voted for tax credits; Hunt said he thought Biden had. Gephardt acknowledged that he had supported them earlier in his career but that "I think we are now at the point where we have to concentrate on making public schools excellent."

According to an NEA legislative report card, Biden voted in 1978 against an amendment that would have deleted tuition tax credits. Biden, informed of the record after the forum, said he did not recall the vote.

Jackson led the others in calling for a reordering of spending priorities, calling for "from 2 to 4 cents of every federal tax dollar" to be shifted from defense to education.

Sen. Paul Simon (D-Ill.) said funds cut from college student aid should be restored and that more aid should come in the form of grants rather than loans. Biden proposed that college loans be repaid as a percentage of gross income, so college graduates could to pursue lower-paying public sector jobs without the burden of high loan repayments. Babbitt said that those who go into teaching should have their student loans forgiven, while those "who become a lawyer or stockbroker should pay it back at prime {rate} plus two."

All of the Democrats took the Reagan administration to task for not doing more on AIDS education: "Not since Herbert Hoover has a president done less when he should have done more," Gore said. He and other Democrats said AIDS victims should not be segregated from the mainstream of society.

Kemp and du Pont both attacked Democrats for "throwing money at problems" but both also dissociated themselves from the education cuts proposed by the Reagan administration.