James Hodgkinson, 66, from Belleville, Illinois, was shot dead by police after opening fire in Alexandria, Virginia on Wednesday.
The officials said investigators don't know what the list of names means, but members of Congress have been briefed.
The Daily Caller reported on Friday afternoon that Hodgkinson had a list of Republicans in his pocket that was recovered by the Federal Bureau of Investigation.
The FBI has contacted one of the men on the list to inform him that the shooting may have been part of a planned assassination attempt and not a random spontaneous act, the Daily Caller reported. Also hurt but released from hospitals were two Capitol Police officers, David Bailey and Crystal Griner, and House GOP aide Zack Barth.
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Investigators studying Wednesday's attack at a suburban Virginia park said Thursday that Hodgkinson had obtained his rifle and handgun from licensed firearms dealers.
"I'm sorry that he did this", she added.
A reporter wanted to know if there was anything she wanted to say to the victims. "There's still a lot of things that can happen, there's still a lot of forks in the road that we may not even see yet", Sava said.
Hodgkinson said repeatedly that she saw no signs her husband was planning violence.
Hodgkinson appeared to be a volunteer with Bernie Sanders' failed presidential campaign, the Vermont senator said shortly after the incident in a statement.
Hodgkinson, who was shot by police and later died, apparently had been living out of his van in Alexandria since March.