President Reagan will ask Congress today to approve and finance a new naval strategy that calls for creation of 15 task forces powerful enough to take on the Soviets in their home waters and to attack targets far inland with cruise missiles launched from reactivated battleships.

Navy Secretary John Lehman called the Reagan blueprint "a major change in naval strategy" and "a very marked departure from the low-threat, pulled-back Navy strategy of the Carter administration."

He acknowledged it would cost many extra billions. A down payment of $4.2 billion will be requested from Congress today in the form of an addition to the existing Carter shipbuilding budget of $6.6 billion. The extra money would finance the start of another Nimitz class nuclear-powered aircraft carrier, a cruiser, two frigates and a submarine, and would also pay to pull the battleships Iowa and New Jersey and the aircraft carrier Oriskany out of mothballs.

Lehman said the Carter administration opted for a more modest shipbuilding program in the belief that "taking on high-threat challenges of the Soviets was too expensive and not necessary."

But the Reagan administration, Lehman said in a breakfast meeting with reporters, has decided to be bolder and prepare battle groups that could go into waters where the Soviet navy is strongest, such as the oceans north of the gap separating Britain, Greenland and Iceland.

The shipbuilding additions would be part of a request for about $33 billion beyond the Carter administration defense budgets for fiscal 1981 and 1982. About $6.5 billion would be added to the $171.2 billion fiscal 1981 request and $26.4 billion to the fiscal 1982 budget of $196.4 billion.

Other officials said that the Navy will get the lion's share of the total defense budget, about 38 percent. The Army's share is 29 percent, and the gap has caused some internal squabbling within the Pentagon.

Lehman said that the Navy should have a fleet of 600 ships, up frolm 456 now. He aruged that enough vaval forces to threaten the Soviets in such strongholds as the Kola Peninsula would help deter them from attacking the North Atlantic Treaty Organization's central front in Europe.

He mentioned 15 task forces; the Navy has 12 carrier task forces now.

"You size your Navy for warfighting," said Lehman in faulting what he contends was an overly cautious stance of the Cautious stance of the Carter administration.

The plan to re-activate the two 38-year-old battleships is the most radical part of the effort to expand the fleet and boost its offensive firepower quickly in remote regions.

According to administration officials, the plan involves loading up to 320 new 1,500-mile-0range Tomahawk cruise missiles -- with some 60-mile-range Harpoon missiles possibly mixed in -- on each battlewagon. The missiles would be used against fixed targets on enemy territory that would otherwise have to be hit by warplanes from carriers.

Since fixed targets are frequently the most heavily defended, the new strategy would presumably cut down the loss of Navy jets to anti-aircraft fire while allowing the carrier planes to go after mobile targets or others that the cruise missiles might not be able to find or reach.

The idea of bringing back the battleships is not new. A group of congressmen championed the idea last year but it was eventually voted down. 'administration officials believe, however, that there will be a big difference this year.

Last year, the plan was portrayed mostly as a way to bring heavy gunfire to bear from offshore to support Marine-style amphibious landings. The Navy, officials said, was enjoined from stressing trhe cruise missile possibilities because the administration was concerned about various arms control implications and about the risk that a push for sea-based cruise missiles could derail a key decision by allies in Europe to accept nuclear-tipped crusie missiles based on their soil. Yesterday, Lehman said he personally did not feel the United States should be constrained any longer by either the first or second strategic arms agreement with Moscow in building up its own arsenal to meet the Soviet threat.

Under the new Navy plan, the cruise missiles on the battleships would carry conventional rather than nuclear warheads. But the missiles themselves would be clearly capable of carrying either kind and thus eventually could become an issue with Moscow if arms control negotiations ever resume.

Officials said there also had been some internal dispute within the Navy, with the aviator faction not too happy about giving up a traditional, if risky, role to cruise missiles.

Officials said it would cost roughly $1 billion to get the battleships and the carrier Oriskany out of mothballs and make the modifications. The Navy would also take older A4 attack planes -- one of the smallest jets ever built -- out of storage and load them on the Oriskany as a way to get extra airborne firepower into a battle without requiring all the trappings of a more modern aircraft carrier.

The New Jersey could be in operation by late 1982 and the Iowa and oriskany a year later, officials said. It would take another year or two, however, before the cruise missiles would be added. Each battleship would take a crew of 1,500, fewer than before because the air defense guns would be removed, and 3,000 would be needed to man the Oriskany. The Navy is already short of skilled enlisted personnel and pilots, but administration officials contended that retention has improved in the last retention has improved in the last several months and that an additional pay raise in the new budget will make it possible to man the new old vessels.