The Pentagon's budget for next year, as now written, includes $20 million to begin buying the Navy a new fleet of anti-submarine helicopters that critics claim will end up costing $4 billion to $6 billion.

Navy leaders contend that the Falklands conflict underscored the need for such a close-in defense, and they dispute the $4 billion to $6 billion cost estimates made by Pentagon civilians.

Critics inside the Pentagon counter that the new helicopter is just a "nice-to-have weapon" that will aggravate the budget and other problems already associated with President Reagan's rearmament program.

Navy Secretary John F. Lehman Jr., in an interview last night, rejected that assertion, declaring his service is really only replacing anti-submarine helicopters that are wearing out.

The helicopter at issue is an aircraft version of the Sikorsky SH60, which the Army calls the Blackhawk. The Navy intends to put six of the new helicopters on each of its 15 aircraft carriers. The Navy so far has beat down those challenging the chopper in Pentagon sessions on the fiscal 1984 budget.

Congress this year was not convinced that the Navy needed the new helicopter and refused to approve seed money. The fiscal 1984 budget, now in the final stages of preparation at the Pentagon, has earmarked $20 million to start the helicopter program.

If purchased, the carrier's choppers would circle the giant ships listening for subs that might have slipped through the outer defenses of planes, escorting destroyers and other anti-submarine helicopters.

The close-in listening for submarines would be done by having each helicopter hover over one patch of ocean after another near the carrier, like a hummingbird going from flower to flower. At each stop, the helicopter would lower a long cord with a can on the end into the water. The can, actually a dip sonar, would send radio waves for miles under the water. The crew in the chopper would hear the radio waves bouncing off objects in the depths.

If the crew heard the distinct reflective sound which comes from a metal object like a submarine, and cross-checked the evidence with other electronic clues, the helicopter pilot could ask permission to fire his torpedoes at the object hidden under the waves. Today's anti-submarine missiles are supposed to be deadly up to six miles.

The six helicopters on each carrier would search the depths for subs within a 25-mile radius. Helicopters based on destroyers and frigates already patrol waters farther from the ship, dropping silent listening devices called sonobuoys that pick up the telltale sounds of subs moving through the water. The ships that escort carriers, and some of the planes that fly from them, also are equipped to combat submarines.

Despite the expensive defense already in place or planned, Navy leaders consider Soviet submarines the biggest threat to carriers and other ships. Given the difficulty of stopping Soviet submarines, Rep. Joseph P. Addabbo (D-N.Y.), chairman of the House Appropriations subcommittee on defense, has argued that it does not make sense for Congress to go along with the Navy and provide the $6.8 billion it is requesting in fiscal 1983 to build two Nimitz-class nuclear carriers.

Lehman has said that carriers are among the most survivable ships in the fleet. If opponents stop the Navy from replacing the old helicopters with new ones to be requested in next year's defense budget, Lehman added last night, "blood is on their hands."

The Navy proposal calls for spending $75 million from fiscal 1984 through 1987 to develop the new anti-submarine helicopter and then produce 175 of them. Lehman, calling the Pentagon's internal cost estimates of $4 billion to $6 billion "ridiculous," said the total will be a fraction of that because the airframe and the electronics to go inside the new chopper are in production.