WASHINGTON (AP) _ The Navy says it will proceed with its effort to end General Dynamics Corp.'s monopoly on Trident submarines, and also try to end a monopoly held by the nation's other sub builder - the Newport News Shipbuilding & Drydock Co.

In a letter dated Jan. 29 and obtained Monay, the Navy rejected the contention of Sen. Christopher Dodd, D-Conn., that it would not be cost- effective to inject competition into the Trident construction program.

Currently, the Navy's large, missile-carrying Tridents are made exclusively by General Dynamics' Electric Boat division, which is based at Groton in Dodd's home state. The Navy has been trying for more than six months to get the Virginia-based Newport News Shipbuilding to bid against General Dynamics for Trident contracts.

''Based on the benefits realized from competing other ship construction programs, we are confident that bringing competitive pressures into the Trident submarine program would have significant cost benefits to the taxpayers,'' the Navy wrote.

It added that its efforts to spur competition will be ''even-handed.''

''We are also planning to compete nuclear refueling work for submarines now performed sole source by either Newport News or naval shipyards.''

The task of overhauling and refueling nuclear submarines is currently divided between Newport News and government-owned shipyards without any type of competition. According to Rear Adm. Stuart F. Platt, the Navy's competition advocate, Newport News has been receiving one to two such contracts each year on a ''sole source'' basis, with each contract worth between $100 million and $150 million.

Newport News had been expecting to begin work within the next month on the latest such contract involving the overhaul and refueling of the Benjamin Franklin, a Poseidon missile-carrying sub that was commissioned in 1965.

Platt said Monday the Virginia shipyard has been notified it must submit a bid on that project. The public shipyard in Charleston, S.C., has also been directed to prepare a competing bid, and Navy officials expect to receive both by the end of the month, Platt added.

Later this year, bids will be solicited on a second such contract, Platt continued. Since General Dynamics has not performed this type of overhaul work for some time, it is unlikely it would submit a bid on the Benjamin Franklin, Platt said.

''But General Dynamics would certainly be eligible to submit a bid on subsequent contracts if it desired to do so,'' added Platt.

''We are trying to keep a check-and-balance between our two submarine yards,'' Platt said. ''We are trying to bring about competition in a sensible manner. We're not favoring one yard over another.''

Neither Newport News nor General Dynamics had any immediate comment Monday on the Navy's letter to Dodd.

Newport News, a division of Tenneco Inc., and General Dynamics currently compete for contracts to build nuclear attack submarines. But General Dynamics is the only source of the much larger Trident.

The Navy has so far purchased 12 of a planned 20 Tridents from General Dynamics. A 13th contract is expected to be awarded to General Dynamics during the current fiscal year, but the company is currently under suspension because of a federal fraud indictment returned in December involving alleged mischarging on an Army contract.

Dodd's spokesman said the senator had not changed his position.

''Our feeling is that midway through a major weapons system of a limited nature, does it make sense for the Navy at this stage of the game to be fostering or subsidizing competition?'' said Paul Allen, Dodd's press secretary.