Attorney General Edwin Meese III announced yesterday that the administration had asked Congress to add $101.6 million dollars to the federal budget for drug enforcement programs for the remaining months of fiscal 1985.

At a news conference with Treasury Secretary James A. Baker III and Transportation Secretary Elizabeth Hanford Dole and several Republicans on the Senate Appropriations Committee, Meese promised "to shake the foundations of deeply entrenched and sophisticated drug empires." He said the additional funds would allow the hiring of 2,000 new agents, attorneys and support personnel to work on drug investigations.

The funds, which would be included in the 1985 Supplemental Appropriations Bill, would include $26.8 million extra for the U.S. Customs Service, $23 million for the Coast Guard, $20 million for the Drug Enforcement Administration, $13 million for the U.S. Marshals Service, and smaller amounts for several other federal law-enforcement agencies.

Earmarked for the remainder of the fiscal year, ending Oct. 1, the funds would supplement the annual drug-enforcement budget of $1.2 billion.

Baker said that most of the new customs funds would go for aircraft and boats equipped with sophisticated surveillance equipment.

Meese told questioners that he could not estimate the amount of illegal drugs circulating in the United States. "Unlike agriculture, drug traffickers don't file crop reports," he said.

Asked why the administration had not cut foreign aid to drug-producing countries, Meese said, "We have a major effort going on in every part of the world. There is no source country that is not cooperating to some extent. We are keeping pressure on those countries."

The proposal to increase drug-enforcement funds is similar to one Democrats on the Appropriations Committee made last month.