President Reagan told a group of religious leaders yesterday that he will push for a revised constitutional amendment to restore voluntary prayer to the classroom when the Senate Judiciary Committee takes up the issue this week.

Reagan earlier had supported an amendment that would overturn Supreme Court decisions of the early 1960s and allow voluntary school prayer. It stated:

"Nothing in this Constitution shall be construed to prohibit individual or group prayer in public schools or other public institutions. No person shall be required by the United States or by any state to participate in prayer."

Yesterday's revision adds the sentence, "Nor shall the United States or any state compose the words of any prayer to be said in public schools."

The Rev. Jerry Falwell, president of the Moral Majority, said after the White House meeting that the revision was designed to attract additional support for Reagan's amendment from senators "who have been borderline for fear that some school board or board of education might compose a prayer and force the students to pray that prayer. It now becomes a matter where parents, children and teachers can decide."

Senate Judiciary Committee Chairman Strom Thurmond (R-S.C.) and others favoring school prayer had been asking the administration to come up with a prohibition on state-drafted school prayer, which resulted in the revised language, according to White House aide Morton Blackwell.

Thurmond is expected to introduce the amendment when the panel meets Thursday, he said.

The committee also is expected to consider another amendment that would allow silent prayer and meditation and the "equal access" right of students to meet voluntarily for Bible study or prayer at school during non-class hours.

Meanwhile, the president yesterday signed a $46.8 billion fiscal 1984 appropriation bill for the Department of Housing and Urban Development, the Environmental Protection Agency and several other agencies.