A House-Senate conference committee yesterday approved a sharply scaled back tuition tax credit bill that would provide tax breaks to parents of college students but deny any relief for private or parochial elementary and secondary school pupils.

The compromise legislation, agreed on after a day-long session that almost ended in stalemate, would allow parents to reduce their taxes by 35 percent of the tuition cost for each student, to a maximum of $100 this year, $150 in 1979 and $250 in 1980.

The write-off would be made available effective this past Aug. 1, in the time to cover the fall semester now under way at most schools.

The decision marked a setback for Catholic school groups, which had lobbied vigorously for extending the credit to parochial schools, and a victory for the Carter administration, which had contended any such move would be unconstitutional.

However, President Carter is still expected to veto the bill as unneeded and too costly. The president told a news conference yesterday he still had "deep concern" over the legislation. The two houses are expected to approve the compromise in time to send it to his desk late next week.

It was not immediately clear whether Congress would sustain a veto if Carter rejected the measure. It passed by a 209-to-194 vote in the house and 65-to-27 in the Senate. Moreover, Congress is heading into the final days of an election campaign.

Yesterday's decision climaxed a day of stubborn wrangling between Senate and House conference over the controversial parochial school issue. The Senate had rejected any aid for parochial school students, but the House added it to the bill when the measure reached the floor there.

However, House conferees were forced to give in when Sen. Russell B. Long (D-La.), chairman of the Senate Finance Committee, threatened to withhold his signature from the conference report if the parochial school credit were included. Long contended the Senate would never support the provision.

The bill approved by the conference committee would cost the Treasury $1 billion in its first full year of operation, compared with $1.2 billion for the House version of the legislation and $2 billion for the Senate bill. The Cost for fiscal 1979, however, is only $400 million.

Long has suggested that a veto of the tuition tax credit bill might be what is needed to prevent the major tax cut bill for individuals and business, now pending in the Senate, from overshooting congressional budget limitations. The larger tax bill has pushed the Senate about $1.3 billion over its budget.

The 35 percent credit was a compromise between a 25 percent figure voted by the House and a 50 percent credit approved by the Senate. The Senate bill also would have provided for a maximum write-off of $500 per student, beginning in 1980.

Yesterday's compromise marked what appears to be the next-to-final chapter in a 1 1/2 year debate over the tuition credit legislation. Carter proposed a rival plan last winter, involving an expansion of existing federal college scholarship programs, but the bill has been bottled up in the House Rules Committee.

The conference committee version would apply only to full-time students this year and in 1979. Beginning in 1980, however, the credit also would be available to part-time students provided they attend half time or more for at least four months.