The Interior Department vowed that its fiscal 1986 budget request will not force the closing of any visitor facilities in national parks, wildlife refuges or other recreational crannies of its far-flung realm, but visitors may feel a pinch in the pocketbook.

From higher fees for park visitors to more cost-sharing by the beneficiaries of multimillion-dollar water projects, President Reagan's budget proposal for Interior is a study in user fees.

States would get about $54 million less in royalties from mineral development on federal lands, for example, because the department wants to deduct its costs of managing the program before sharing receipts with the states.

Prospective bidders on offshore oil leases would have to pay for required geologic and geophysical data. The government picks up the tab for that information now.

Ranchers would have to pay more to graze cattle on federal land, and abandoned mine reclamation efforts would be curtailed because revenues from an industry tax are not keeping pace with expenditures.

The Bureau of Reclamation would start only three new projects, chosen because sponsors have indicated a willingness to pay a larger proportion of the construction expense.

A nickel here, a few million dollars there, and it all adds up to a 15 percent reduction in the department's budget. Reagan requested $5.7 billion for Interior, compared with $6.6 billion in 1985.

The budget would prune $217 million from the Bureau of Reclamation, where some projects would be "stretched out" to reduce expenses next year. The move would mean delays in some, among them the massive Central Arizona Project, which would take two additional years to deliver water to Tucson.

The National Park Service budget would be cut about $240 million, but most of that would come from a proposed moratorium on buying new parklands. That idea that has been unpopular on Capitol Hill in the past.

The Bureau of Land Management would be $156 million lighter, but much of that stems from a proposed transfer of 19 million acres of BLM land to the Agriculture Department. The transfer requires congressional approval, however, and initial reaction from lawmakers has not been encouraging.

Similarly, the Interior budget deletes $85 million in aid to Micronesia and the Marshall Islands, on the assumption that Congress will approve a new compact for those trust territories and the burden will shift to the State Department.