Attorney General Jeff Sessions was asked in a letter released Friday to investigate claims that Russian state-sponsored hackers masqueraded as Islamic State terrorists to harass the relatives of U.S. military personnel.

Sens. Ron Wyden, Oregon Democrat, and Cory Gardner, Colorado Republican, wrote Mr. Sessions this week regarding a May 2018 news report involving CyberCaliphate, a purported Islamic State hacking group credited with sending death threats in early 2015 to several American military spouses.

Published as the result of a lengthy investigation conducted by The Associated Press, the report said that a Russian government hacking group known by names including APT28 and Fancy Bear had harassed the spouses while posing as members of the Islamic State, also known as ISIS.

“We write to express our concerns about reports that Russian intelligence services posing as Islamic extremists threatened and harassed U.S. military families,” the senators wrote to Mr. Sessions. “We urge you to investigate this potential false flag operation and to hold any perpetrators accountable.

“If substantiated, the claims about APT28 posing as the Cyber Caliphate could be the first public evidence that influence operations have specifically targeted American military families,” they wrote. “If left unchecked, such operations would threaten the personal liberty, financial security, mental health, and morale of our military families.”

Five of the military spouses who were targeted in 2015 were quoted in a CNN article published weeks earlier after the same supposed Islamic State group took credit for breaching the Twitter account of the U.S. Central Command.

One of the spouses resides in Oregon and the other in Colorado, Mr. Wyden’s office said Friday.

The Department of Justice did not immediately return an email seeking comment.

Mr. Wyden released the letter to Mr. Sessions shortly after the Justice Department announced criminal charges Friday against a dozen Russians accused of hacking targets during the 2016 U.S. presidential race, including the Democratic National Committee and John Podesta, the chairman of Hillary Clinton’s 2016 presidential campaign.

GRU, a Russian military intelligence agency, employed hackers who “conducted large-scale operations” with the goal of meddling in the 2016 race, according to Friday’s indictment. The Russian hacking group accused of breaching the email account of Mr. Podesta is the same that targeted U.S. military spouses, AP reported previously.