Sen. Mark Udall, D-Colo., who serves on the Senate Armed Services and Intelligence committees, said he would review the guidelines to ensure they keep "with our values as a nation," but indicated lawmakers may ask for additional overtures.
"I commend the president for his effort to define the boundaries of U.S. counterterrorism operations and for stating a commitment to increased accountability," Udall said. "While this is helpful and important, more needs to be done."
Relevant congressional committees are already notified when drone strikes occur. But it's unclear how the administration, under Obama's new transparency pledge, will handle public notifications, particularly when Americans are killed.
The public only knew about the deaths of three Americans by drone strikes through media reports and the fourth when Attorney General Eric Holder disclosed it in a letter to Congress on the eve of the speech.
Under current policy, the official U.S. figures of number of strikes and estimated deaths remain classified.
According to the New America Foundation which maintains a database of the strikes, the CIA and the military have carried out an estimated 416 drone strikes in Pakistan and Yemen, resulting in 3,364 estimated deaths, including militants and civilians. The Associated Press also has reported a drone strike in Somalia in 2012 that killed one.
The think tank compiles its numbers by combining reports in major news media that rely on local officials and eyewitness accounts.
Strikes in Pakistan spiked in 2010 under Obama to 122, but the number has dropped to 12 so far this year. Strikes were originally carried out with permission of the Pakistani government of Pervez Musharraf, though subsequent Pakistani governments have demanded strikes cease.
The CIA and the military have carried out some 69 strikes in Yemen, with the Yemeni government's permission.
Associated Press writer Sebastian Abbot in Islamabad contributed to this report.
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