An NRA spokesman said members of the lobbying group were simply "doing our jobs."
"With these robocalls, the NRA has stooped to a new low in the debate over how to best protect our kids and our communities," Democratic Sens. Richard Blumenthal and Chris Murphy wrote to NRA Executive Vice President Wayne LaPierre after receiving complaints from hundreds of residents.
The residents, who also spoke to the local press, said they were bombarded with calls asking them to contact their state legislators to oppose passage of a state bill that would "disarm and punish law-abiding gun owners and sportsmen."
The state Legislature is drafting stricter gun-control measures that would ban so-called assault weapons and magazines with more than 10 bullets and would require "universal background checks" on all gun sales.
Newtown resident David Freedman, who said he received a robocall last week, told the Hartford Courant, "I have never supported the NRA [and] I never will -- even being a Republican."
Mary Ann Jacob, a Sandy Hook Elementary School librarian who rushed 18 students into a supply closet the morning of the Dec. 14 shooting that killed 20 first-graders and six adult staff members, told The (Danbury) News-Times she received at least three calls last week as well as a postcard she said she threw into the trash.
The phone messages, she said, described how state Rep. Mitch Bolinksy, a Republican lawmaker whose district includes only Newtown, was "trying to take away your Second Amendment rights."
"Put yourself in the shoes of a victim's family member who gets calls at dinnertime asking them to support more assault weapons in our school and on our streets," the senators' letter said.
"In a community that's still very much in crisis, to be making these calls opens a wound that these families are still trying hard to heal," it said.
NRA spokesman Andrew Arulanandam told the Courant the Washington lobby, which promotes the right of citizens to bear arms, is not targeting Newtown but has been "mailing and phoning our members and supporters all over Connecticut for the past two months" to keep them "abreast of the latest developments regarding their rights in the state Legislature."
"We're just doing our jobs," he said.
In a separate statement, Arulanandam said Connecticut NRA members, contributors and supporters "expect us to ... keep them abreast of developments on the legislative front in their state."
"We provide the same service for our members and supporters all around the country," his statement said.
Arulanandam did not say if the NRA intended to change its tactics -- tactics Blumenthal said in a news conference Monday appeared both "calculated and intentional."
"They've disregarded and disrespected the victim's families and an entire community that continues to grieve," Blumenthal said. "Everyone impacted by this tragedy deserves a profound and immediate apology."