The Reagan administration has asked Congress to transfer $60 million to the Coast Guard from various highway proj-ects, Amtrak and mass-transit operating subsidies in an effort to end a slowdown of safety and drug-interdiction patrols brought on by a budget shortfall.

Transportation Secretary James H. Burnley IV said in letters to the House and Senate Appropriations transportation subcommittees that even with the extra money, the Coast Guard will be $43 million short of its needs this fiscal year. This will be made up through savings from previously announced base closings and by deferring maintenance, training and spare-parts purchases, according to Adm. Paul A. Yost, the Coast Guard commandant.In addition to those cutbacks, the Coast Guard has reduced routine patrols by 55 percent. The additional money would "enable us to end the slowdown in Coast Guard operations, increase drug interdiction, search and rescue and fisheries enforcement patrols," according to a statement by Yost.

However, the request may not sit well with Congress, which originally held down the Coast Guard budget to compensate for the administration's failure to fund Amtrak and its proposed cuts in mass transit. House and Senate members who inserted highway projects in the budget also are likely to fight for them.

A senior Senate staff member said it is "too early to tell" what Senate reaction will be, but the request "contains some politically sensitive things that may cause problems" in the House.

Key committee chairmen were not available for comment.

The administration's proposed cuts in current fiscal year funds include:

$25.3 million in highway proj-ects, including access roads to recreational lakes in several Western states, a highway in the Virgin Islands, a project to close expressway gaps in the Davis-Woodland, Calif., area and a railroad consolidation project to eliminate highway-rail interference in Orange, Texas. Some of the projects could be funded through the highway trust fund, where they would have to compete with other projects, a spokesman said.

A $12.4 million 2 percent reduction in Amtrak appropriations.

A $17.3 million 2 percent reduction in mass-transit operating assistance.

Because some of the affected proj-ects were to be spread over several years, the long-term cut would amount to about $175 million, according to the Senate aide.

The administration called its request "reprogramming," but it was sent to Capitol Hill as a supplemental appropriations request. That means it will be considered by Appropriations committees and subcommittees before being merged into supplemental-appropriations legislation for the current fiscal year, expected to work its way through Congress in the coming months.

The battle is expected to be fought over the same grounds when Congress considers the fiscal 1989 budget that President Reagan just sent to the Hill, which also would eliminate Amtrak and cut other popular programs such as mass transit.