A divided Senate Finance Committee yesterday approved a tuition tax credit bill after adding strong anti-discrimination provisions that liberals had insisted upon but some groups seeking the credits oppose.

The committee action was a victory for President Reagan, who had pressed for it. But the bill, approved 11 to 7, still seems unlikely to be enacted; House and Senate leaders have both said they doubt it can pass this year.

Finance Chairman Robert J. Dole (R-Kan.) acknowledged as much. Asked about prospects, he said after the committee session, "I'm just following the urging of the president. He hasn't been here long enough to know that Congress can't do things."

The anti-bias language, which is also stronger than the administration first wanted, would give the Internal Revenue Service as well as the Justice Department an enforcement role.

Fundamentalist Christian and some other groups supporting tuition tax credits strongly oppose giving the IRS such powers. The administration also had wanted enforcement solely by the Justice Department.

The committee voted Wednesday for a joint enforcement provision put forward by Sen. Bill Bradley (D-N.J.).

But Dole said he would not send the bill to the floor with the Bradley amendment because it would be "doomed."

Dole then suggested a compromise, which the administration and Bradley accepted yesterday. Bradley withdrew his amendment, but it was agreed the tuition tax credit program would not take effect until it is also made clear, in a related issue, that the internal revenue code forbids tax-exempt status for any private school that practices racial or other illegal discrimination.

This could be done by the Supreme Court in a case before it or, failing that, by Congress.

The tax-exempt issue arose when the administration last January reversed an established IRS policy of denying such status to schools that discriminate racially. The president said the IRS lacked the authority to take such actions.

The administration has since half-reversed itself and introduced legislation to give the IRS such power. Meanwhile, the issue has also gone to the Supreme Court, where arguments are scheduled for October.

Under the provisions of yesterday's bill, parents who send their children to private elementary and secondary schools could claim half the tuition as a tax credit beginning in the second half of 1983, up to a maximum credit of $100, if the anti-discrimination language is in place by then. The maximum credit would rise to $300 by 1985. Under Reagan's original proposal, it would have risen to $500.

The Reagan proposal would have phased out the credit for families with incomes between $50,000 and $75,000 a year. But the committee voted yesterday to phase out benefits for families with a gross adjusted income between $40,000 and $50,000. Families with higher incomes would not be eligible.

Sen. John H. Chafee (R-R.I.) proposed denying benefits to parents whose children attend schools that discriminate against the handicapped. The administration opposed the change, and the amendment was watered down to provide that private schools involved in the tax credit program cannot discriminate against the handicapped in admissions, but they would not be required to provide special facilities or teachers for handicapped children.

The administration also opposed efforts by Sen. Harry F. Byrd Jr. (Ind.-Va.) to attach an amendment to deny benefits to students in coed private schools that practice sex discrimination. His proposal would parallel law now in effect for schools that receive federal money, but he was defeated.