Sen. Warren B. Rudman (R-N.H.), who is backing the presidential candidacy of Sen. Robert J. Dole (R-Kan.), said yesterday he had pushed for immediate release of a new White House note on the role of Vice President Bush in the secret Iran arms sales because "it would have been worse if it had been leaked."

The question of Rudman's instrumental role, and the White House handling of the episode, have for the second time this week underscored the political sensitivity to actions by the president's advisers that could hinder the presidential campaigns of the two leading GOP candidates. Just as the new Iran note was being released, Bush and Dole forces were haggling over the role of President Reagan in the senator's announcement Thursday of his support for the INF Treaty.

The new note said Reagan and Bush "are solid" in favor of the Iran arms sales in February 1986 and has rekindled interest in the vice president's position and advice to Reagan during what became the gravest foreign policy crisis of the Reagan presidency.

Rudman, who was vice chairman of the Senate Iran-contra committee and is Dole's chairman in New Hampshire, said, "I'm for Dole, but I wouldn't do anything to hurt the vice president." He said he had told White House counsel Arthur B. Culvahouse Jr. on Monday that the new note and two others would have to be declassified and made public.

"I assumed he would notify the vice president and I told him it would be worse if they took a long time in getting them out," Rudman said.

On Monday, Culvahouse did notify Bush aides of the possible release. Then, on Tuesday morning, White House chief of staff Howard H. Baker Jr. told the vice president and the president, in their regular morning meeting, that congressional investigators had seen the documents, but there was no indication they would ask for the notes to be declassified and made public, according to an official familiar with Baker's conversation.

But later that day, the request to release the document was made. Another White House aide said the document was actually declassified later that same day. Congress was informed the note was cleared for release on Wednesday morning, according to Senate sources.

Although Bush aides said they had no objection to release of the note, they also said they had been led to believe by Baker that it would not be declassified. The White House controls whether to declassify such documents. The official familiar with Baker's remarks said he gave Bush no such assurances.

Asked yesterday while campaigning in New Hampshire about the timing of the release of the new document, Bush said, "I have no comment on the release of that information. I'd like to not think there's something conspiratorial about it. I hope not. I don't have any evidence. You're asking the wrong guy."

The notes emerged from a sophisticated search of National Security Council computer files which had been erased by former national security adviser John M. Poindexter. A total of 96 notes were recovered, some of which had not been available to the congressional investigations into the Iran-contra affair.

The note mentioning Bush was written by Poindexter on Feb. 1, 1986, to former national security adviser Robert C. McFarlane, and talked of hostages being released by Feb. 9. Poindexter wrote the note two weeks after the president had approved the first direct U.S. shipment of arms to Iran as part of a plan to release American hostages held in Lebanon.

The Bush note is significant because the vice president has given different descriptions of his own role in the affair. The note also indicates that Bush was supporting a covert operation which directly contradicted the official U.S. public policy of not making concessions to terrorists. Bush was advocating this policy in the report of his task force on combating terrorism, which was drafted at the same time the Iran arms sales were being approved and carried out.

The congressional investigation was unable to document in detail Bush's role in the deliberations on whether to sell arms to Iran. For instance, after key meetings in January 1986, the final report said, "There is no record that the vice president expressed any view."

Arthur Liman, who served as chief Senate counsel and reviewed the new documents Monday morning, said yesterday that the Feb. 1, 1986 note describing Bush's position "really stood out because we had never found any document that said what the vice president's position was. Had we gotten it before, we would have quoted it in our report."

Rep. Lee H. Hamilton (D-Ind.), chairman of the House Iran-contra panel, said, "We do not yet have from the vice president a full and complete explanation of just how he viewed the sale of arms to Iran."

Bush maintained yesterday that, at the time of the Poindexter note, the United States was not considering a swap of arms for hostages. "The deal was not arms for hostages at that time. The president never would have approved an arms for hostages deal," he said in a radio interview.

In the note, however, Poindexter told McFarlane, "The hostage plan is still working and it calls for the hostages to be released on 9 Feb."Staff writer Lloyd Grove contributed to this report.