US Secretary of State John Kerry has urged the Nigerian army to show restraint and not violate human rights as it pursues an offensive against Islamist militants in the north-east.
Mr Kerry said there were "credible allegations" of "gross human rights violations" by the Nigerian military.
This week Nigeria launched its biggest offensive since the Boko Haram group began its insurgency in 2010.
A state of emergency is in force in Adamawa, Yobe and Borno states.
"The United States condemns Boko Haram's campaign of terror in the strongest terms," Mr Kerry said in a statement.
"We urge Nigeria's security forces to apply disciplined use of force in all operations, protect civilians in any security response and respect human rights and the rule of law.''
More than 2,000 people have died in the violence since 2010, most of which is blamed on Boko Haram.
On Friday Nigerian war planes and helicopter gunships attacked several militant training camps in the north-east, officials said.
One plane was hit by anti-aircraft fire, but Brig Gen Chris Olukolade said it had returned to base safely, while the "terrorist base" was subsequently "completely destroyed".
This is the first time Boko Haram has been reported to have used such heavy weaponry against aircraft.
A resident in Maiduguri, the capital of Borno state, told the BBC that the city was unusually quiet on Friday, with most people staying inside.
Brig Gen Olukolade said "several thousand" troops had been sent to the three north-eastern states to tackle Boko Haram.
The three semi-desert states where the state of emergency has been declared border Niger, Chad and Cameroon. They are roughly the size of England or the US state of Illinois but have a population of just 10 million.
Last month, Boko Haram rejected the prospect of an amnesty suggested by President Goodluck Jonathan.