But Human Rights Watch said the evidence it had gathered "strongly suggests" that the strikes in Yemen it documented "did not adhere" to the policies set out by Obama.
The group said the attacks its report covers took place between 2009 and 2013, killing 82 people, at least 57 of them civilians.
The strikes ostensibly targeted suspected members of al Qaeda in the Arabian Peninsula (AQAP), but victims included women, children, truck drivers and other civilians, the report said.
"At least four of the strikes were carried out by drones, a fifth strike by either drones or warplanes, and a sixth one by cruise missiles releasing cluster munitions, indiscriminate weapons that pose unacceptable dangers to civilians," it said.
The report also questioned the military validity of several of the suspected al Qaeda operatives targeted.
Fear and polarization
Both reports describe the climate of fear created by the drones in Pakistan and Yemen, and the polarizing effect the attacks are having on local populations.
"The ultimate tragedy is that the drone aircraft the USA deploys over Pakistan now instill the same kind of fear in the people of the Tribal Areas that was once associated only with al Qaeda and the Taliban," said the Amnesty report.
"Like other forces operating in the Tribal Areas, the USA appears to be exploiting the lawless and remote nature of the region to evade accountability for its violations," it said.
Human Rights Watch described a similar situation in Yemen.
"We Yemenis are the ones who pay the price of the 'war on terror,'" Faisal bin Ali Jaber, a relative of a cleric and a police officer who were both killed in a drone attack in August 2012, was quoted as saying in the report. "We are caught between a drone on one side and al Qaeda on the other."
The report warned that "should the United States continue targeted killings in Yemen without addressing the consequences of killing civilians and taking responsibility for unlawful deaths, it risks further angering many Yemenis and handing another recruiting card to AQAP."
'A dangerous precedent'
The reports set out a list of recommendations, primarily for the U.S. government, but also for authorities in Pakistan and Yemen.
More broadly, Amnesty warned that the American government may be setting a troubling standard in its use of drones that other countries could follow.
"U.S. policy and practice on targeted killings and drones are not only of concern in their own right: they also set a dangerous precedent that other states may seek to exploit to avoid responsibility for their own unlawful killings," the report said.
In Yemen, images of the charred, shattered remains of the cleric and policemen killed in August 2012 have circulated in the village where the attack took place, the Human Rights Watch report says.
"Now when villagers see these images," Jaber, the relative, was quoted as saying, "they think of America."