A majority of the Republican-controlled Senate wants to reach agreement on deficit reductions before acting on President Reagan's top-priority tax revision bill, Majority Leader Robert J. Dole (R-Kan.) said yesterday.

Dole stopped short of linking the two issues in a way that would hold tax-overhaul hostage for a budget agreement, but said chances for the tax measure would be enhanced by a deficit-cutting budget accord.

"If we had a deficit-reduction bill agreed to, it really would help the tax bill," Dole said.

Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) put it more strongly, suggesting that Reagan would be more likely to compromise on the budget if tax overhaul was not yet in hand.

Dole's comments were in reaction to a letter being circulated by Sen. Rudy Boschwitz (R-Minn.) that seeks to use the tax bill as leverage to nudge the White House into a budget agreement.

The Boschwitz letter also seeks to assure that any new revenue, such as receipts from a proposed oil import fee, be used for deficit reduction rather than to offset rate reductions in the tax-overhaul measure.

Apparently distressed at reports of the letter, White House chief of staff Donald T. Regan came to Capitol Hill in the late afternoon to meet privately with Dole, Domenici and Boschwitz.

"They White House officials weren't too thrilled with the letter," Boschwitz said.

Boschwitz and Domenici told reporters later that Regan assured them the White House would work to meet Congress' timetable for action on the budget and said he did not think a budget-before-taxes letter would be helpful.

But the two senators said they intend to continue circulating the letter. "I think we're going to go forward," Boschwitz said. Asked how many signatures the letter had received, Boschwitz laughed and said "roughly enough to make an impact now," apparently referring to Regan's trip to the Hill.

Regan made no comments to reporters as he left the meeting.

Dole also stepped up pressure on the White House to cooperate on the budget by warning that Congress is unlikely to push ahead with painful deficit reductions to meet the targets of Gramm-Rudman-Hollings budget-balancing legislation unless it has White House cooperation.

"If they just sit it out, they may find the House and Senate sitting it out too," Dole said. Referring to Senate Republican initiatives on deficit reduction that were undercut by the White House last year, he told a reporter later, "We gave it the old college try last year and found out they closed the school."

Underscoring the same point, House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) and House Budget Committee Chairman William H. Gray III (D-Pa.) reiterated their refusal to support tax increases unless Reagan moves first.

"Unless the president gets out front and says we need revenue to curb the deficits, it a tax increase ain't going to happen," Gray said. "I'll support a tax increase only if the president of the United States presents it," said O'Neill.

Gray also contended it would take a congressional budget gridlock to create public pressure on Reagan to abandon his opposition to tax increases.

He predicted that Republicans will be ready to "confront" Reagan on the issue by late summer when they will face possible loss of the Senate in a backlash against deep spending cuts. The cuts will be triggered by Gramm-Rudman-Hollings unless a budget compromise is reached to achieve a deficit of $144 billion for fiscal 1987, which would require spending cuts or tax increases of about $40 billion.