The 600-ship Navy has run aground on budget shoals.

Navy officials said yesterday that they have run into such a spending crunch that President Reagan's goal of leaving behind a 600-ship Navy will not be realized until the next decade, if then.

A Navy budget proposal now being considered by top Defense Department officials calls for retiring 16 frigates, leaving 589 ships available for deployment in 1990 rather than the projected 605.

The Navy's recommendation calls for eight to be taken from the Atlantic Fleet and eight from the Pacific Fleet, with half of them going out of service in the current fiscal 1988 and the rest in fiscal 1989, which begins Oct. 1.

Besides saving unspecified billions of dollars, the ship retirements would ease a Navy manpower shortage, which skippers say is becomming severe. Overall, the Navy is not short on sailors but the skippers say it is running critically short of such skilled petty officers as boiler tenders and machinist mates, who are needed to man ships at sea.

The proposed ship retirements represent fresh evidence of how the military is restructuring itself to accommodate the big cuts Congress has made in the defense budget over the last three years. Three years ago, then-Navy Secretary John F. Lehman Jr. said the 600-ship Navy was too far along for Congress to stop. The numbers at the time bore him out.

Navy Secretary James H. Webb Jr. has said that the Navy should receive a bigger portion of the Pentagon's funding than other services because of its worldwide deployments. However, Army, Air Force and Marine leaders, also strapped for funds, will fight any Navy campaign to reapportion the budget.

Webb has said that if more money is not forthcoming, U.S. policymakers should reassess military commitments around the world with an eye to withdrawing from some of them. This proposal, in the absence of increased military spending by NATO partners, is not expected to get far, Pentagon officials said.

If the 16 frigates are retired early, Navy leaders said the warships left will have to stay at sea longer on escort duty. The Navy goal has been to limit sea deployments to six months and allow crews to stay at home for 12 months before returning to sea.

With fewer ships, deployments will be longer than six months, Navy leaders said, unless the service is relieved of some of its obligations in the Persian Gulf and elsewhere. A return to long deployments will probably discourage reenlistments, aggravating the manpower problem, they said.