Navy leaders are pushing to shore up the ailing company that builds the Trident submarines by settling millions of dollars in back claims, some of which Adm. H. G. Rickover says may be fraudulent.

The Navy fears that the Electric Boat Co., of Groton, Conn., will not be able to continue working indefinitely on the Trident and on attack submarines of the 688 class unless the government comes through with some money in a hurry.

Electric Boat executives claim that the government owes them $544 million for unanticipated cost increases.

Rickover, in a Dec. 2 memo to Edward Hidalgo, assistant secretary of the Navy for manpower and logistics, warned that the claims may be fraudulent and that the Navy Claims Settlement Board should be allowed to adjudicate them.

Rickover wrote Hidalgo that he was preparing reports on fraud by shipbuilders, "including a report on apparent fraud in the Electric Boat claims."

Hidalgo is chairman of the Navy's "Special Steering Group" recently established to negotiate a settlement with Electric Boat, a division of General Dynamics.

A Navy spokesman said last night that the discussions between the Hidalgo board and Electric Boat "could conceivably lead" to the Carter administration seeking emergency financial relief for the shipyard under Public Law 85-804.

However, the Navy spokesman added, that emergency help will not be decided upon until after face-to-face discussions between the Hidalgo board and Electric Boat executives.

Last year, in an effort to unsnarl the tangled relations between the Navy and its shipyards, then-Deputy Defense Secretary William P. Clements Jr. asked congressional approval to advance money to the yards.

But in the face of congressional opposition whipped up in part by Rickover, the Pentagon withdrew its request. The effort to extend emergency relief may be renewed this year, which could pit President Carter against his old mentor, Adm. Rickover.

The $544 million Electric Boat claims the Navy owes the yard stems from work on 11 of 18 nuclear attack submarines of the 688 cross under contract.

As the argument drags on over who owes whom how much of that $544 million. Electric Boat has complained, the company is under the "intolerable" burden of pouring $15 million a month into the yard.

Electric Boat recently laid off 3,000 employees. The yard said layoffs stemmed not from the disputed claim but from moving out of paperwork and into construction of the attack subs.

Politicians around Groton have been lambasting both the Navy and Electric Boat recently for not doing something fro the unemployed workers.

Settlement of the $5.44 million in claims or emergency payments allowed under federal law would ease the financial pinch of Electric Boat. But this money would not mean hiring back the people laid off, according to company officials.

Backover, besides warning Hidalgo in his memo that some of Electric Boat's claims may be phoney, said taking the issue out of the hands of the Navy claims board will undercut negotiations with Newport News Shipbuilding Co.

Newport News, which is building nuclear-powered cruisers and aircraft carriers for the Navy, also claims it is owed millions of dollars for extra work.

"Newport News," Rickover wrote, "will interpret the Navy's action in assigning the Electric Boat claims to another group as evidence that the Navy is pursuing a settlement with Electric Boat independent of the merits of their claims.

"No doubt," Rickover continued, "the company will harden its position in dealing with the [Navy Claims Settlement] Board, thus making it increasingly unlikely that the board can settle the Newport News claims on their merits."

Newport News, when asked to bid on building the first Triden submarine, said it would do so only if the Navy covered the actual costs of building the lead ship rather than setting a fixed price in advance.

The Navy turned to Electric Boat. The price of the lead Trident has increased from the estimated $800,000 to at least $1.2 billion, according to the Navy.