President Reagan yesterday renewed his vow to oppose any tax increase as the White House tried to squelch talk of possible new taxes among members of the Senate Budget Committee.

Reagan is "as strong as 10 pounds of onions" against a tax increase, White House spokesman Larry Speakes told reporters. "If there is one thing he is adamant on, it is no -- and I repeat -- no new taxes."

A senior White House official, who was interviewed on condition he not be identified, said "we're not going to be pushed into a corner" on tax increases. "The president is amazed to hear this talk so soon after the election. He thought that during the debates and the like, that he had pretty well put that issue to rest."

The comments followed a legislative strategy meeting at the White House Monday. Reagan's top advisers concluded at the session that they had to quickly dampen the talk of possible tax increases in the Senate Budget Committee.

The Republican-controlled panel, while voting for a one-year freeze on defense spending, has rejected many of Reagan's domestic spending cuts, proposed to reduce the deficit, and deadlocked over Social Security cost-of-living adjustments. One possibility raised at the White House legislative strategy session would be more personal involvement by Reagan, who has been focusing on the MX missile recently and devoting less attention to lobbying on the budget.

The president may bring small groups of senators to the White House to push for budget cuts, officials said.

"This is the opening gun," the senior official said.

Speakes issued a point-by-point rationale from the White House for why a tax increase should be avoided, citing the strength of the economy and specifically ruling out new levies on corporations, energy and consumers. However, Speakes said Reagan had not ruled out "loophole closings."

Senate Majority Leader Robert J. Dole (R-Kan.) issued a warning against tax increases yesterday. In a press release from Geneva, where he is observing the opening round of U.S.-Soviet arms talks, Dole said tax increases are "not in the mix" for this year's budget.

"Once we start down the tax path, spending cuts will be left in the dust," Dole said. "We have to keep our eye on spending cuts and more spending cuts until we have absolutely exhausted that option."

Reagan "admits that the deficit is large and that it is difficult to cut the budget, but nevertheless it must be cut -- that's the only proper way to handle the deficit," the senior official said. "The raising of taxes is bad from most any angle you could look at."