President Reagan asked Congress yesterday for authority to obligate $280.5 billion and to spend $245.3 billion in fiscal 1984 for defense, record amounts he said are required to build a military strong enough "to prevent both nuclear and conventional war."

The requests represent increases of 14 percent in both budget authority and spending. Domestic spending, by contrast, is budgeted to rise only about 2 percent in a year when inflation is expected to be about 5 percent. Many in Congress have said they are upset at this unevenness. Republican leaders already have said they will try to cut Reagan's defense request by up to $20 billion.

Defense Secretary Caspar W. Weinberger, indicating that he knows he is in for his biggest fight yet in trying to hold the line on the president's program to rearm America, said at a Pentagon budget briefing that major reductions in the Reagan recommendations would strip the nation of much of its muscle.

A $15 billion cut in proposed spending, Weinberger said, would require cancellation of all planned orders in 1984 for the Army AH64 helicopter, Navy F14 and F18 fighter planes, Trident missiles and Los Angeles attack submarines, and Air Force F15 and F16 fighters, C5 transports and MX and cruise missiles.

In drawing that line, Weinberger, on behalf of the president, challenged Congress to find places to cut which would not kill politically popular job-producing weapons programs, reductions in the number of Army divisions or decrease the readiness of the Army, Navy, Air Force and Marine Corps to fight.

Weinberger gave the argument he is expected to sound all year in defending the military budget: "A decade of neglecting investment in defense has forced us to accept double duty. First, we have had to act quickly to increase the basic readiness and sustainability of our forces, so that we could meet an immediate crisis if one arose. At the same time, we must make up for lost years of investment by undertaking the research and development and force modernization needed to meet threats that may arise in the future."

He dramatized that rationale with charts to be shown to Congress and other audiences all year comparing how the Soviets, even under the Reagan budget, will be outproducing the United States in everything from tanks to warplanes to battlefield nuclear missiles.

Specifically, Weinberger gave this comparison of Soviet and U. S. weapons production for fiscal 1984: tanks, 1,920 to 720; armored vehicles, 4,070 to 750; artillery and rocket launchers, 1,480 to 190; tactical warplanes, 680 to 330; warships, 9 to 3; attack submarines, 7 to 3; missile submarines, 3 to 1, and theater nuclear missiles, 650 to 340.

Besides trying to persuade Congress of the need for spending $245.3 billion on national defense in fiscal 1984, Weinberger confirmed that he will send Congress a supplemental request for $1.6 billion in the current fiscal year to retrieve funds deleted by Congress last year for the MX, Pershing II and cruise nuclear missiles and for force of U S. troops in West Germany.

To offset this request in part, Weinberger said he would request permission from Congress to rescind $650 million previously approved for other programs. These rescissions must be approved within 45 days after being submitted to Congress. Defense officials said the timing and composition of these two requests are still under deliberation within the administration.

The Reagan Pentagon's decision to put hardware over manpower is underscored in the new breakdown of where the dollars would go in fiscal 1984, if the president's blueprint is adopted.

Specifically, $94.1 billion is earmarked for buying weapons compared with $47.9 billion to pay and feed military people. Weinberger acknowledged that his early plans to expand the the All-Volunteer Force by about 200,000 people have had to be shelved to release extra money for hardware.

No other account in the Reagan military budget shows a jump comparable to the $64.1 billion to $94.1 billion between fiscal 1982 and 1984. Research and development, which holds money for tomorrow's weapons that are financed in the procurement account, showed the next biggest increase in that period, from $20.1 billion to $29.6 billion.

Weinberger had both good and bad news for the 2.1 million men and women in uniform. He said they would not receive the projected 7.6 percent October raise for fiscal 1984, since Reagan included the military in the general government personnel pay freeze, but would get a catchup increase this time next year for fiscal 1985.

By current Pentagon reckoning, this would mean a raise of about 11 percent in October, 1984.

Chairman John G. Tower (R-Tex.) introduced a bill yesterday to give a 4 percent raise to everyone in the active military except the first two enlisted grades and the first officer rank, effective April, 1984. He said this raise for half the fiscal year would cost $552 million.