One day after Republicans picked him to be the Senate's new majority leader, Sen. Robert J. Dole (R-Kan.) sent the White House a powerful signal of independence yesterday, declaring that he favors an across-the-board budget freeze as an alternative to deep but selective spending cuts the president outlined to congressional Republican leaders earlier in the day.

While emphasizing that he is "not looking for a fight with the president," Dole left little doubt in an interview yesterday that he will play a more forceful, outspoken role than his predecessor, retiring Sen. Howard H. Baker Jr. (R-Tenn.), in challenging White House proposals that are unpalatable to the Senate.

Speaking of deep domestic spending cuts outlined earlier in the day at a White House meeting, Dole said: "It's not possible to do that. We ought to be looking at a broader approach, a freeze."

While there may have to be some increases for defense and programs that help the poor, spending as a whole may have to be frozen below current levels to get deficits down to $100 billion within three years, as the administration wants, Dole said.

"It may not be the best policy but sometimes you have to sacrifice a little policy to get something passed . . . . I'm prepared to support it," he added.

Later in the day, after Hill Republican leaders had left, Reagan endorsed a freeze concept.

Dole's election over four rivals by the 53-member Senate Republican majority Wednesday was widely interpreted as indicating that the Senate wanted an aggressive defender of the chamber's prerogatives in relations with the White House, and Dole acknowledged that he was aware of his GOP colleagues' assessments.

They wanted the White House to know "we got elected because we're fairly intelligent individuals and we have some pretty good ideas that may not occur to some people downtown who may not even have been elected to anything," he said.

But Dole also took pains to make it clear he would attempt to pass administration proposals when they do not conflict with Senate interests, saying, "I don't have any real problem with the White House."

Among other things, he said, he was prepared to give early priority to the confirmation of Edwin Meese III, President Reagan's counselor, as attorney general.

He reserved judgment on two issues that will come back before Congress in early spring: renewal of U.S. aid to the "contra" forces fighting the Sandinista government of Nicaragua and further production of MX intercontinental ballistic missiles.

But Dole said he thinks Senate support for the Nicaraguan rebels may have increased in the wake of reported communist-bloc arms shipments to the Nicaraguan government.

He also said he thought the White House would look seriously at the spending freeze proposal, although he acknowledged that Reagan was noncommittal about it during yesterday's leadership meeting.

"I think it's going to get explored," Dole said.

Dole's support for a freeze was particularly important in light of the fact that he, along with other leadership figures, opposed a bipartisan freeze advanced last year by his fellow Kansas Republican, Sen. Nancy Landon Kassebaum, and several others.

"There were enough votes to pass the freeze last year had not a lot of us supported the president's program," Dole said yesterday in reference to the "Rose Garden" plan for about $144 billion in deficit reductions over three years.

Most of the reductions were enacted, but deficits still are expected to hover around $200 billion a year through most of the rest of the decade unless spending cuts or tax increases are enacted.

Dole reemphasized that deficit reductions are "No. 1" in priority for the Senate next year. But he expressed strong doubts that tax increases will be seriously considered in light of Reagan's opposition to them and gave no indication that he would lead any charge to raise taxes, even though he did so in previous years.

Buoyant in the wake of his victory, Dole even took some cheer from his critics, noting that conservative fund-raiser Richard Viguerie called his election "an unmitigated disaster, something like that." But even Viguerie may benefit, Dole suggested. "I think I'll help him raise some money. He'll send out a mailing saying how bad I am.