The Senate Finance Committee yesterday approved, 11 to 7, a bill to give tuition tax credits to parents of children in private schools.

Opponents, saying the bill would weaken the nation's already hurting public schools, immediately threatened to filibuster when it hits the Senate floor.

The committee vote was a victory for President Reagan, who campaigned in favor of tuition tax credits in 1980. In a letter to the committee, he argued the credits, long sought by Catholics and some but not all other private school groups, would create "competition" between public and private school systems, prompting both to "improve the quality of education they offer."

Sen. John H. Chaffee (R-R.I.), a leading opponent, charged, however, that the legislation would divert federal money to private schools at a time when public schools are in particular need, while simultaneously encouraging the brightest children to transfer from public to private schools.

"This diversion of federal funds will profoundly weaken our public school system," Chaffee said. "There is not one thread of evidence that the private schools of the nation are endangered in any way."

When fully in effect in 1985, the legislation would cost the federal government from $700 million to $800 million a year in lost tax revenues.

Sen. David L. Boren (D-Okla.), another opponent, said "it may take 11 votes to get it out of committee, but is going to take at least 60 votes" to get it through the Senate. He was warning that the legislation faces a fillibuster, which could be stopped only if 60 senators vote to do so.

The legislation would provide benefits for any person earning less than $40,000 a year with a dependent in elementary or secondary private school. The credit would be half the tuition for each child, up to a maximum credit of $100 for the year starting July 1, 1983, $200 the next year and $300 thereafter.

For poor persons who pay no taxes, the credit would be refundable, meaning the government would send the parent a check.

For those with incomes above $40,000, the amount of the credit would phase out until it reached zero at $50,000.

The House has taken no action on a tuition tax credit bill.