The National Security Agency has sent a letter to its employees' family members, in an effort to "reassure" relatives about the agency's work.

The letter, signed by NSA director General Keith Alexander and deputy director John Inglis, is dated 13 September and is addressed to "NSA/CSS family". It characterises press reports of NSA overreaches as "sensationalised" and laments how stories published on documents leaked by Edward Snowden have seen the agency portrayed "as more of a rogue element than a national treasure".

"We are writing to you, our extended NSA/CSS family, in light of the unauthorized disclosure of classified information by a former contractor employee," says the letter, which was published on The Dissenter website on Friday. "We want to put the information you are reading and hearing about in the press into context and reassure you that this Agency and its workforce are deserving and appreciative of your support."

The NSA has been under scrutiny since details of its surveillance programs were revealed by the Guardian and other outlets. The agency has been criticised for collecting Americans' phone and internet data, in what some see as a breach of the fourth amendment.

"Some media outlets have sensationalized the leaks to the press in a way that has called into question our motives and wrongly cast doubt on the integrity and commitment of the extraordinary people who work here at NSA/CSS – your loved one(s)," the letter says. "It has been discouraging to see how our Agency frequently has been portrayed in the news as more of a rogue element than a national treasure. You've seen the dedication, skill and integrity that those employees bring to their job each and every workday, contributing to the accomplishments of the agency over the past 61 years."

The message is aimed at providing a morale boost to NSA staff and their families while also providing talking points and rebuttals to criticisms of the agency. Alexander and Inglis write that they will continue to provide employees with "materials they can bring home to help you understand that our activities are lawful, appropriate and effective".

The letter repeats a claim previously made by the agency that its activities "contributed to keeping the nation and its allies safe from 54 different terrorist plots".

That claim has been repeatedly challenged, including by senators Mark Udall and Ron Wyden. In June, Udall and Wyden, both members of the Senate intelligence committee, said they had "not yet seen any evidence showing that the NSA's dragnet collection of Americans' phone records has produced any uniquely valuable intelligence".

The letter acknowledges that the NSA has erred in the past, but insists there is a system in place for the reporting of such errors.

"In concert with our mission, NSA/CSS employees are trained from the first day on the job, and regularly thereafter, to respect the privacy and civil liberties of US citizens. We go to great lengths to achieve our goal of no mistakes. However, we are human and, because the environment of law and technology within which we operate is so complex and dynamic, mistakes sometimes do occur.

"That's where the unique aspect of our culture comes into play. We self-report those mistakes, analyze them, and take action to correct the root causes."

Alexander and Inglis add that such mistakes are reported to "our oversight bodies in the Congress, the Foreign Intelligence Surveillance Court and the executive branch, where appropriate".

The message signs off by thanking family members of employees for their "continued support and encouragement". Relatives of NSA employees are "an integral part" of the agency's success in defending America, Alexander and Inglis write, adding: "We have weathered storms before and we will weather this one together, as well."