The White House told Senate Republican leaders yesterday that President Reagan remains firm in his opposition to tax increases in the next fiscal year but will give the Senate leadership "running room" to put together a 1984 budget resolution that can command a majority vote.

Reagan personally reinforced the message on taxes as he left for Camp David, Md., saying he is "prepared to veto" any tax increase Congress approves. "I don't think at this stage of the economic recovery that increasing taxes can do anything except hinder the recovery," he said.

The president's comments came in the wake of Thursday's rejection by the Senate of a budget resolution that would have preserved Reagan's July tax cut but included high future deficits.

The Senate also rejected an alternative sponsored by Slade Gorton (R-Wash.) and backed by GOP moderates that would have raised $8.9 billion in new taxes next fiscal year, presumably by limiting Reagan's tax cut. The budget resolution then was sent back to the Budget Committee under rules to report out another version by the middle of next week.

After meeting privately with senior presidential aides yesterday, Budget Committee Chairman Pete V. Domenici (R-N.M.) said that taxes will have to be increased above the small amounts proposed for fiscal 1984 and 1985 in Reagan's budget, but added: "I think it is important that we keep those numbers in those two years as low as possible."

Domenici, joined by Senate Majority Leader Howard H. Baker Jr. (R-Tenn.), Finance Committee Chairman Robert J. Dole (R-Kan.) and Sen. Paul Laxalt (R-Nev.), met at the White House with chief of staff James A. Baker III, Office of Management and Budget Director David A. Stockman and other presidential aides to discuss the Senate budget impasse.

Howard Baker and Domenici were described by sources as determined to get a budget resolution through the Senate next week, even if the measure does not dovetail entirely with Reagan's goals.

The White House aides reportedly told the senators that Reagan could not accept any major tax increases in 1984 and 1985, but the president would give them "running room" to get a bipartisan budget resolution through the Senate.

Asked whether he is willing to compromise on the budget, Reagan said yesterday, "I have compromised for two years now." But he said he is "prepared to be reasonable."

Questioned whether he would prefer to have no congressional budget resolution than one increasing taxes, as a White House spokesman indicated earlier this week, Reagan replied:

"The budget resolution is meaningless to them Congress . They've never abided by that. But I would rather, even so, see them demonstrate to the business and industrial and financial community that they are willing to be responsible and proceed with the cutting of government spending and recognize that the tax cut so far is the incentive that has brought about the recovery."

Administration sources said Reagan would wait to see what comes out of a House-Senate conference before deciding whether to embrace the budget resolution.

Domenici is said to believe that the outcome next week will be similar to the Gorton alternative that was defeated this week and which included $8.9 billion in new taxes in fiscal 1984, $14 billion in 1985 and $51 billion in 1986.

Reagan objects to tax increases in the first two years, but he originally proposed a "standby" tax increase in the third year.

Martin Feldstein, chairman of the president's Council of Economic Advisers, said yesterday that a fiscal 1984 tax increase in the range of $9 billion "will neither make nor break the recovery." But other administration officials suggested that it was doubtful that Reagan would accept such a tax increase.