Faced with growing pressure from Senate Republicans for an early budget compromise this year, President Reagan yesterday held fast to his demands for defense spending increases, domestic budget cuts and no tax increase to reduce the deficit.

"Any tax increase the Congress sends me will be DOA -- dead on arrival," Reagan said from Camp David in his weekly radio address.

Reagan also announced, as expected, that he ordered federal agencies to start across-the-board spending cuts required under the new balanced-budget law.

Passage of the law "was an admission by the Congress that zero hour is upon us," Reagan said. The $11.7 billion spending cut for the current fiscal year, 1986, is to take effect March 1, barring a successful court challenge, and will equal a 4.3 percent cut for domestic agencies and 4.9 percent for defense. Reagan said government services could be maintained despite cuts, but complained "these budget savings make no distinction between high priority programs and those of little merit." Reagan was given permission this year to shield military personnel and his missile defense program from the cuts.

Reagan is to submit his fiscal 1987 spending plan Wednesday, and members of his party in the Senate are eager to avoid another year of inaction on the deficit.

The president's reaffirmation of his priorities came as Senate Republicans circulated a letter urging him to act on deficit reduction this year before tax revision. In a series of private breakfast meetings recently, the Republicans urged Reagan not to wait until August or September to reach a compromise on reducing the deficit.

Some White House officials have said recently that Reagan may be willing to reach such a compromise and have pointed out that the defict outlook has improved recently. To meet the fiscal 1987 targets set by the Gramm-Rudman-Hollings law, about $38 billion in deficit savings is now estimated to be required, compared to estimates of nearly $60 billion a few weeks ago.

But others in the Reagan Cabinet, such as Defense Secretary Caspar W. Weinberger, think he should hold out against any deal that would further slow the military buildup.

Yesterday, Reagan offered no ground to lawmakers who would like to strike a three-point bargain: domestic cuts, a slowdown in the defense build-up and a tax increase.

Without being specific, Reagan said he will propose eliminating some domestic programs and transferring others to state and local government, but he said Social Security payments and "essential" support for "anyone who needs" assistance would not be affected.

Reagan insisted on "modest but steady growth" in the defense budget, but stopped short of mentioning his proposal in the budget for a 3 percent increase in military spending above inflation, a growth rate that many on Capitol Hill say he has no chance of winning.

"The Soviets want nothing more than to see America flinch and forsake the rebuilding program we've worked so hard to get started," he said. "We've spent five years making our military more competitive and America secure again. We must not permit this vital work to be undone in the second term."

On raising revenues, Reagan said, "We haven't built 37 months of economic expansion and created over 9 million jobs by raising taxes on the people."

Reagan opened his radio address with a tribute to the astronauts killed in Tuesday's explosion. "This has been a difficult week for the United States," he said. "I know we've all been deeply shaken by the tragedy of the space shuttle Challenger."