"Since at least 2013, the Nigerian military has conducted a secret, systematic and illegal abortion program in the country’s northeast, ending at least 10,000 pregnancies among women and girls," the news agency said.
"Many had been kidnapped and raped by Islamist militants," it said, adding that those who resisted an abortion ran the risk of being "beaten, held at gunpoint or drugged into compliance."
Northeastern Nigeria is the epicenter of a jihadist insurgency launched by the Boko Haram group in 2009 that has killed more than 40,000 people, displaced around 2 million and spread beyond the nation's borders.
The report was based on witnesses from 33 women and girls, five health workers and nine security personnel involved in the alleged program and on military documents and hospital records "describing or tallying thousands of abortion procedures."
Most of the abortions, Reuters said, were carried out without the woman's consent and some were conducted without their prior knowledge through abortion-inducing pills or injections passed off as medications to boost health or combat disease.
In its reaction, the Nigerian army lashed the report as "a body of insults on the Nigerian peoples and culture."
"Nigerian military personnel have been raised, bred and further trained to protect lives," it said.
"(The) Nigerian military will not, therefore, contemplate such evil of running a systematic and illegal abortion program anywhere and anytime, and surely not on our own soil."
United States on Wednesday said it was seeking more information, according to State Department spokesperson Ned Price.
"My reaction to it in the first instance was a personal one in that I read it and was deeply disturbed by it," he said.
"It was a harrowing report. ... It's a concerning report and for that reason we are seeking further information," he said.
Religion plays a core part in Nigerian life, with Islam the dominant faith in the north of the country and Christianity in the south.
Abortion is illegal except when the mother's life is in danger.
In the north of the country, illegal pregnancy termination carries the risk of a 14-year jail term.
Some information for this report came from Reuters.