The Republican-controlled Senate, frustrated at President Reagan's refusal to negotiate over next year's budget, voted 72 to 24 yesterday to oppose consideration of tax overhaul until he reaches a budget agreement with Congress.

With the support of the GOP leadership, senators approved a nonbinding resolution stating "the sense of the Senate that tax reform should not be considered by the United States Senate until a firm, definite budget agreement has been reached between the president and the Congress of the United States."

The move was opposed by Senate Finance Committee Chairman Bob Packwood (R-Ore.), who called it "insane and inane" and vowed to continue his committee's mark-up of a bill to revise the nation's tax laws.

"If we are going to put a hold on all bills until we get a budget, we'll have a whale of a September," Packwood said in reference to the month that Congress intends to complete its work before adjourning for the congressional elections.

The vote was the latest of several assertions on the part of the Senate that deficit reduction is more important than tax reform. It was also an expression of mounting frustration at the administration's refusal to compromise on defense spending, taxes and other critical budget issues.

For some, it also appeared to signal misgivings about the tax-revision effort, especially to the extent that new revenues are to be used to cut tax rates rather than to reduce the deficit.

Senators on both sides of yesterday's vote said they thought the Senate should move ahead on the budget without waiting for the White House. "We cannot afford to wait around week after week for the White House to decide whether it wants to talk," said Sen. J. Bennett Johnston (D-La.), who voted for the budget-before-taxes proposal.

The resolution, sponsored by Sens. Rudy Boschwitz (R-Minn.) and Steve Symms (R-Idaho), who earlier recruited half the Senate to sign a letter to Reagan making the same point, was one of several moves during the day aimed at breaking the budget out of its stall.

Earlier in the day, Senate Majority Leader Robert J. Dole (R-Kan.) and House Minority Leader Robert H. Michel (R-Ill.) sent a letter to House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) urging that the House and the Senate move in tandem to consider the budget. They also proposed negotiation of a timetable for completion of the budget by both houses.

The Democratic-controlled House has been waiting for the Senate to move first on the budget, and Dole has been holding up action on a Senate Budget Committee draft because many Republican senators oppose it. The committee proposal defies Reagan by proposing tax increases, slashing his defense request and rejecting many of his cutbacks in domestic programs. The White House has labeled it unacceptable.

The Dole-Michel letter was seen as an effort to get around election-year fears that could prevent either party from considering controversial moves, such as tax increases, that many consider necessary to get a budget that will meet the deficit-reduction targets in the new Gramm-Rudman-Hollings law.

"If we're going to walk off this plank," said Dole in explaining the letter to his colleagues, "I'd like to have some company."

Democrats, led by Sen. Howard M. Metzenbaum (Ohio), pushed and then backed off from a proposal to direct Dole to bring up the committee budget proposal as the Senate's next order of business.

Dole declined to commit himself to a specific date for bringing up the measure but indicated that he will do so when he could produce a "truly bipartisan" budget, meaning at least as many Republicans as Democrats voting for it. The budget, he assured Metzenbaum, is "certainly a matter of priority."

Metzenbaum dropped his proposal after it became clear that Republicans and some Democrats would oppose the move as a violation of leadership prerogatives.

All but seven of the 50 Republicans voting supported the budget-before-taxes proposal; almost two-thirds of the 46 Democrats voting supported it. Among Washington-area senators, only Paul S. Sarbanes (D-Md.) opposed it.