"It is vitally important, however, for the Congress and the American public to have a full understanding of how the executive branch interprets the limits and boundaries of this authority so that Congress and the public can decide whether this authority has been properly defined and whether the president's power to deliberately kill American citizens is subject to appropriate limitations and safeguards," according to a letter the lawmakers sent to Obama on Monday.

The letter is signed by Sens. Ron Wyden, D-Oregon, Mark Udall, D-Colorado, and Susan Collins, R-Maine, of the Intelligence Committee as well as Mike Lee, R-Utah; Chuck Grassley, R-Iowa; Jeff Merkley, D-Oregon; Dick Durbin, D-Illinois; Patrick Leahy, D-Vermont; Tom Udall, D-New Mexico; Mark Begich, D-Alaska; and Al Franken, D-Minnesota.

Dianne Feinstein of California said in a statement that the Justice Department memo and other information has permitted the Intelligence Committee to conduct "appropriate and probing" oversight into the use of lethal force.

"That oversight is ongoing, and the committee continues to seek the actual legal opinions by the Department of Justice that provide details not outlined in this particular white paper," Feinstein said.