President Reagan asked Congress yesterday to increase defense spending by 16 percent between this fiscal year and next as part of a $1.3 trillion buildup in the nation's defenses over the next five years.

Defense Secretary Caspar W. Weinberger, presenting the request to a supportive Senate Armed Services Committee, said: "Our proposed increases would significantly and quickly strengthen our ability to respond to the Soviet threat at all levels of conflict and in all areas of the world vital to our national interest."

He conceded under questioning by Sen. John W. Warner (R-Va.) that Reagan's revision of former president Carter's defense budgets for fiscal 1982 and beyond assumes a lower rate of inflation than Carter projected.

But Weinberger insisted this assumption's is a good bet and promised, if the administration is incorrect, to ask Congress for extra money to buy the missiles, ships, planes and tanks included in Reagan's five-year plan.

The Reagan administration virtually took the Carter shopping list and ordered more of the same weapons rather than place a different kind of order with the nation's defense contractors. An exception was the addition of $2.5 billion to finance a new manned bomber to penetrate Soviet defenses.

What kind of bomber should be purchased is a question the Pentagon will study until June. An update of the B1 bomber, which Carter rejected in favor of cruise missiles and the "Stealth" designed to be invisible to enemy radar, are the leading candidates.

The Army, under additions made to the Carter shopping list, would receive more money for its Blackhawk helicopter, Roland and Divad antiaircraft weapons and infantry fighting vehicle.

The Navy would receive an extra $4.2 billion for ships, including two patrol frigates, a cruiser, an attack submarine and a down payment on a Nimitz nuclear aircraft carrier.

The Air Force would receive $575.7 million to buy A10 attack planes built in Hagertown and extra money to increase its purchases of F15 fighters; and the Marines would get a down payment for an amphibious assault ship.

Because of additions to Carter's fiscal 1981 and 1982 defense budgets, it is now estimated that military spending will jump from $158.6 billion to $184.8 billion between those years, an increase of 16.5 percent, believed to be a record hike between two peacetime budget years.

An Office of Management and Budget spokesman said last night that the spending increase under the Reagan defense budget would be slow, amounting to only $4.8 billion more for fiscal 1982 than would have been the case under the Carter budget. He asserted that the military spending boost is not disproportionate to cuts proposed by Reagan in several domestic programs.

Because money set aside in one year's Pentagon budget is not actually spent for several years, the amount shown as the total obligational authority is substantially larger than the spending figure.

Reagan seeks congressional approval to obligate $178 billion in fiscal 1981 and $222.2 billion in fiscal 1982, an increase of 24 percent. Those totals represent net increases of $6.8 billion and $25.8 billion in the Carter budgets for fiscal 1981 and 1982.

In fiscal 1982 through 1986, Reagan would spend $1.289 trillion and obligate $1.460 trillion.

From fiscal 1983 onward, Reagan is striving for an annual after-inflation growth of about 7 percent compared to 5 percent set as an objective by the Carter administration in response to Congressional pressure.

John G. Tower (R-Tex.), chairman of the Senate Armed Services Committee, indicated yesterday that he wants the Pentagon's major budgets approved by congress before there is any backlash about cuts in domestic programs.

Urging Weinberger to finish several reports Congress has requested as quickly as possible, Tower said: "My rationale for a full-court press will be more apparent later."

A senior Air Force official said Tuesday that if Reagan failed to win congressional approval of cuts in domestic programs, the Pentagon would probably have to regroup and cut its budget to help bring total government spending under control. The Pentagon budget has been virtually off-limits to the administration's cutback experts.

In hopes of capitalizing on what Reagan administration leaders sense is a favorable climate toward higher defense spending even as social programs are reduced, Pentagon civilian leaders will soon launch a public relations offensive.

Weinberger and the civilian service secretaries will be the point men in the offensive that is to feature television appearances and speeches detailing a growing Soviet threat.

Weinberger revealed part of the script yesterday in a Pentagon press conference and his Senate appearance:

Military pay. Those in uniform will receive a 5.3 percent pay raise in July atop the 11.7 percent raise already approved for fiscal 1981. They will receive at least an additional 9.1 percent in fiscal 1982.

"Our military personnel will become first-class citizens once again," Weinberger pledged.

SALT talks. "Rarely in history have we or any great nation pursued such noble goals, risked so much and yet gained so little" as has been the case under the arms control agreements known as SALT I and SALT II, Weinberger said.

"This administration remains committed to equitable and verifiable arms control" but is "abandoning unwarranted illusions," he said. Instead, he continued, the administration will "consult our allies shortly to design a realistic approach" to arms control.

MX land missile. The administration intends to press full-speed-ahead with the missile but is not sure how it should be deployed. Weinberger has said he fears envvironmental suits would stop the project if the Carter plan to base 200 MX missiles in the valleys of Nevada and Utah is pursued.

Industrial base. Reinvigorating the defense industry will receive top priority, with spreading shipbuilding contracts to more yards one possibility.

Sen. Henry M. Jackson (D-Wash.) called it "just outrageous" for the Trident missile submarine to be two years behind schedule in the Electric Boat yard in Groton, Conn., and urged Weinberger to build "a more competitive shipyard base."