The Senate, unable to agree on limiting debate on the Supreme Court nomination of Judge Robert H. Bork, yesterday postponed the opening of the Bork debate until at least Tuesday.

Senate Majority Leader Robert C. Byrd (D-W.Va.) announced the decision and said that resolution of the Bork nomination could be further delayed depending on the outcome of an unrelated battle over administration policy in the Persian Gulf.

Byrd said that when the Senate reconvenes on Tuesday, it will first vote to limit debate on the Persian Gulf dispute. If this cloture motion succeeds, the Senate will continue on the Persian Gulf issue until it is settled, Byrd said. If the cloture motion fails, Byrd said he will move immediately to the Bork nomination even though he has failed to reach agreement with Senate Republicans for a deadline to vote on confirmation.

Meanwhile, one of the handful of conservative Senate Republicans who object to a deadline for a vote, Sen. Gordon J. Humphrey (R-N.H.), denied at a news conference that he is seeking to delay action on the Bork nomination until after the National Conservative Political Action Committee (NCPAC) completes a telephone campaign urging support for Bork and contributions to its depleted coffers.

"It's silly to suggest that my request for adequate time is somehow related to fund-raising," said Humphrey, NCPAC's honorary chairman. "It's absurd."

Byrd on Thursday linked Republican resistance to setting a deadline to vote on the Bork nomination to the NCPAC telephone campaign. "How much money do they need?" he said in suggesting the timing of the debate would be determined by NCPAC's fund-raising goals.

The telephone campaign began Sunday, two days after Bork conceded that his nomination is doomed, and is to conclude Tuesday. Humphrey yesterday acknowledged that the Senate seems certain to reject the nomination, but he said a full-scale floor debate would provide Republicans with a "political issue" they could use against Democrats in next year's elections.

Two other Republicans, Sens. John Heinz (Pa.) and Alfonse M. D'Amato (N.Y.), announced yesterday that they will vote to confirm Bork. D'Amato called Bork "the president's choice," adding that he hopes President Reagan would next "nominate someone who represents the best of the Reagan revolution, and who will be confirmed quickly."

Six senators have not formally announced a position on the Bork nomination and 54 are publicly committed to vote against it.

Reagan told law enforcement officials yesterday that Bork's opponents are promoting an agenda "to protect criminals."