The letter comes as American strikes in Pakistan, Yemen and Somalia, and the example the United States has set for the world, are drawing intense scrutiny. United Nations human rights investigators are reviewing the American record, and Congress has shown a new willingness to discuss the classified program in public, with a House subcommittee hearing on the constitutional and counterterrorism implications of targeted killing set for April 23. That hearing was postponed for a week in an effort to persuade the administration to send an official to testify, a committee aide said.

Caitlin Hayden, a spokeswoman for the National Security Council, said the administration was “committed to institutionalizing and explaining to the Congress and the public as much as possible about our drone policies, including the process for making strike decisions.” She added: “Our approach is marked by scrupulous adherence to the rule of law.”

By the count of the New America Foundation, a research group that tries to track targeted killing, the United States has carried out 422 strikes in Pakistan and Yemen, 373 of them since Mr. Obama took office in 2009, in addition to a handful in Somalia. The foundation estimates the number of deaths resulting from the strikes to be between 2,426 and 3,969, of which about 10 percent were of civilians and nearly as many of which were identified as “unknown.” An overwhelming majority of the strikes have been carried out by unmanned drone aircraft, though cruise missiles, fighter jets and helicopter gunships have also been used.

Agreeing to the degree of openness sought by the human rights groups would mean a sea change for the Obama administration. Though officials have given a series of careful speeches on the administration’s legal reasoning, the Justice Department’s classified legal opinions on the subject have been shared only recently, even with the Senate and House Intelligence Committees, and the government has asserted in battling Freedom of Information Act lawsuits that the Pakistan strikes are too politically delicate even to be officially acknowledged.

Gabor Rona, the international legal director of Human Rights First, said that the letter to Mr. Obama reflected increasing concern that government secrecy has hidden grave legal and practical problems with the strikes.