Senate Republican leaders announced an agreement with the White House yesterday to end a 10-year battle over the financing of harbor, dam and related water projects by requiring local governments and private users to pay a major share of future costs.

The deal, which anticipates prompt Senate action on permanent cost-sharing legislation, opens the way for White House approval of down payment money this year for 25 water projects that would ultimately cost about $4 billion.

A down payment of $63 million, as proposed in a spending bill for the rest of fiscal 1985 that was approved by the Senate Thursday night, would break a decade-long drought in water-development financing, caused in large part by the dispute over cost-sharing.

These initial projects, including harbor improvement efforts for Baltimore and Norfolk that, together, could cost nearly $1 billion before completion, would be financed under funding agreements based on cost-sharing guidelines set in the White House-Senate agreement.

Such project-by-project agreements would have to win the approval of top federal officials, virtually assuring compliance with the new cost-sharing principles. Moreover, agreements would have to be worked out within a year or the funding would expire.

The House has passed legislation that would finance 35 projects with start-up costs of $71 million but without cost-sharing provisions.

Although the administration will not demand a similar long-term cost-sharing agreement with House leaders, officials said yesterday that they will insist on the Senate restrictions for whatever start-up projects are approved.

Though the two chambers have sharp differences over water-project financing that have blocked revision efforts in the past, the outlook for agreement on the start-up projects is enhanced by the pent-up demand for water money. "There is a powerful thirst out there," said one administration official.

The White House-Senate agreement provides for local or state governments or users to pay 20 to 60 percent for harbor construction, with the higher percentage applicable to such deep-water ports as Baltimore and Norfolk, and 30 to 40 percent for harbor operations and maintenance. A tax of 0.04 percent would be levied on the value of imports and exports going through the ports to finance operational costs.

The nonfederal contribution for flood-control projects would be 25 to 35 percent.

Cost-sharing would also apply to inland waterway projects, but the administration had to back down from its demand for large new user fees under pressure from the powerful but financially distressed barge industry. An 8 cents per gallon fuel tax would rise as scheduled to 10 cents later this year, but no further increase would occur until 1988; starting in 1988 the tax would rise in 10 years to 20 cents.

Half of new construction costs for such waterway projects as locks would be financed from the Inland Waterway Trust Fund financed by the fuel taxes.

Other nonfederal contributions would range from 35 percent for irrigation and beach erosion to 50 percent for recreation to 100 percent for hydroelectric costs.

There is no estimate of how much the new system would save the federal government, which has traditionally borne virtually all the costs of federal water projects. One reason is that, with local governments and private users being asked to shoulder a big share of the costs, the demand for water projects is expected to subside, according to administration and congressional officials.