"The American people should be given basic facts about mistakes when they are made, and they should also be given the rules that the government must follow when targeting and killing an American involved in terrorist activities," Sen. Ron Wyden, D-Ore., a committee member, said in a statement.
The proposed restrictions, however, part of a broader intelligence bill, may not survive. Republicans on the Senate panel voted for the bill, but most opposed the drone amendments. Key lawmakers in the GOP-controlled House also oppose the provisions.
The White House has yet to take a position. Caitlin Hayden, spokeswoman for the National Security Council, said the administration already was transparent concerning drones.
"The president has committed to undertaking these activities with the greatest possible transparency, and we will continue to share as much information as possible with the American people, the Congress and the international community," she said.
In a speech in May at National Defense University, Obama said he had signed a policy directive that set new standards before the White House would approve targeted killing by drones.
Obama said the CIA had to show that a proposed target posed a "continuing imminent threat" to Americans, rather than a "significant threat," the previous standard. In addition, no attack would be ordered without "near certainty" that civilians would not be harmed, the president said.
The number of strikes already had fallen before May, but the new rules served to cut the frequency further.
The Long War Journal, which tracks drone attacks through local news reports, has counted 22 strikes this year in Yemen, down from 42 last year. It has counted 25 attacks in Pakistan this year, down from 46 last year and a peak of 117 in 2010. A single strike has been reported in Somalia this year.
Administration officials have said drone strikes have killed relatively few civilians, but have refused to say how many. The Long War Journal says 11 civilians have been killed in Pakistan this year and two in Yemen; other estimates are higher.
In June, a drone-launched missile hit an SUV carrying a Qaida commander in Yemen. CIA officers didn't realize that his younger brother also was in vehicle, according to U.S. officials who would not be named because the operation is classified. The CIA later put the victim's age at between 6 and 13.
The CIA has given a classified briefing to Congress on the death, but has refused to acknowledge it publicly. The NSA's Hayden declined to comment.
Sen. Dianne Feinstein, D-Calif., chairwoman of the Senate Intelligence Committee, said the number of noncombatant deaths was "significantly lower" than critics claimed. She said she had urged the White House to disclose the data "so the American people know how careful these strikes have been."
In part, drone strikes have declined because there are fewer identified terrorist leaders to hit. In Pakistan, the core leadership of the Qaida network founded by Osama bin Laden has been decimated, although remnants are still active.
But experts say the Nov. 1 drone strike that killed Pakistani Taliban leader Hakimullah Mehsud, who helped organize the suicide bombing that killed seven CIA officers and contractors in December 2009 in eastern Afghanistan, proves that drones remain a vital counter-terrorism weapon.