Administration officials said yesterday that President Reagan has approved a $245 billion defense budget for the coming fiscal year, an increase of 15 percent over this year's level.

The $245 billion is in so-called obligational authority, the right to spend money over several years. This is the best measure of the dimensions of the defense budget. Actual Pentagon spending next fiscal year would be $215 billion, up 18 percent from this year's likely total.

The new figures remain subject to minor revision, but they are a clear and forceful continuation of Reagan's policy of raising the defense budget while cutting back domestic programs. The figures are likely to provoke the sharpest congressional debate yet over administration priorities, partly because 1982 is an election year for one-third of the Senate and everyone in the House.

The president's $245 billion request for defense for fiscal 1983 is $32 billion above the fiscal 1982 obligational authority of $213 billion. The 1982 total includes a planned request of about $6 billion in supplemental funds for military pay and $7.1 billion for military construction--building barracks, air strips and other facilities for the armed services.

By assuming that the inflation rate will not run over 8 percent in the new fiscal year, Reagan's recommended 15 percent increase in obligational authority makes good on his pledge to keep making "real" defense increases of 7 percent annually to improve the military balance with the Soviets.

The sharper rise in actual defense spending, from $182 billion in fiscal 1982 to $215 billion in 1983, stems from pay increases and big bills falling due for stepped-up production of tanks, planes, ships and missiles.

Critics who have reviewed Reagan's new defense budget say that more programs have been started than the services will be able to pay for in future years, meaning further political struggles and possible cancellations could be just over the horizon.

The Army is in particularly bad shape in this respect, they say, because it is trying to buy too much too soon, including the XM1 tank at $2.7 million a copy, an advanced but vulnerable attack helicopter whose cost is skyrocketing, a new generation of armored personnel carriers, and a whole new family of battlefield missiles.

The General Accounting Office, after reviewing Army modernization plans last year, came to a similar conclusion. Because it is committing so much of its money to getting weapons built, the Army could well end up without money to keep them in fighting condition, the watchdog agency warned in a theme now being sounded by Pentagon specialists who reviewed the fiscal 1983 defense budget.

Besides the costs of financing the Army's biggest modernization since World War II, the defense budget was driven up by Reagan's plans to build toward a 600-ship Navy; modernize the Air Force through big purchases of F15 and F16 fighters; fulfill the Marines' request for more ships and for the AV8B Harrier jump jet; and upgrade strategic nuclear forces by setting aside billions for the first seven B1 bombers, the MX land-based missile, and cruise missiles.

Some specific weapons requested within Reagan's fiscal 1983 budget, which will go to Congress next month, are:

* Aircraft carriers: The Navy would get $1.3 billion toward two more of the Nimitz class, in addition to three already built and one under construction.

* Submarines: Two more Los Angeles class nuclear attack submarines costing about $600 million each and another Trident with a price of about $2 billion.

* Warplanes: The first seven B1s, costing up to $400 million each by Congressional Budget Office estimates; 84 F18 and 27 F14 Navy fighters; 120 F16 and 42 F15 Air Force fighters; 18 Marine AV8B jump jets.

* Airlifts: The administration will again try to convince Congress to approve the building of a new long-distance CX military cargo plane. Between $150 million and $200 million would go toward buying the C17, winner of the Air Force CX competition. Cash incentives also are earmarked within the budget to encourage commercial airlines to order wide-bodied jets with bigger doors and stronger floors so these planes could be mobilized for the military in an emergency.

One of the few military policy questions Reagan still has not answered, administration officials said yesterday, is whether to continue to require 18-year-old males to register for the draft, which he opposed as a candidate. The Selective Service System's new budget cannot be closed until the registration issue is settled.