"Each week that passes we learn of more brutal Boko Haram abuses against civilians," the group's Nigeria researcher, Mausi Segun, said in an emailed statement.
"The Nigerian government needs to make protecting civilians a priority in military operations against Boko Haram."
HRW estimates that at least 3,750 civilians died during Boko Haram attacks in 2014 and that the deaths in the first quarter of this year were up on the same period 12 months ago.
Establishing exact tolls of the dead and injured in the brutal conflict is fraught with difficulty, with poor communications in northeast Nigeria and independent travel dangerous.
The Nigeria Security Tracker, run by the US think tank the Council on Foreign Relations, attributes 2,268 deaths to Boko Haram and "state actors".
There is variation, too, in the overall numbers of people killed since the start of the insurgency in 2009, and all are largely based on media reports rather than official figures.
President Goodluck Jonathan said last year that more than 13,000 people had died, although some groups put the figures as few as 9,000 and as high as 17,500.
Nigeria has been criticised for its response to the insurgency and only recently began a concerted fight-back with the help of coalition partners Niger, Chad and Cameroon.
HRW said the rise in civilian deaths came as Boko Haram spread its violence across borders since February and increased suicide attacks on "soft" targets such as markets and bus stations.
Segun also said that Nigerian security forces had "failed to take all feasible precautions" to protect civilians during operations.
It cited civilians as alleging that security forces attacked and burned down the village of Mundu in Bauchi state, in December, killing five local people, including an 80-year-old blind woman.

Shots of destroyed homes in Mundu featured in a video attributed to Boko Haram offshoot Ansaru, entitled "Investigations of the Nigerian Army", posted online on February 11.
"This kind of terrorist act and non-regard to human rights was repeated in Mundu, Bauchi state, under the guise of attacking" Boko Haram, the video message said.
The Nigerian Army said they were unaware of the incident when HRW contacted them but had ordered an investigation, the rights group said, calling the probe "an important first step".

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