Freedom Watch, based in Washington, argues the task force held illegal meetings with lobbyists and gave inadequate public notice, the Washington newspaper The Hill reported Wednesday.
"President [Barack] Obama and Vice President [Joe] Biden have thumbed their nose at the law and instead have been holding closed-door meetings with special interest lobbyists on both sides of the issue," said Freedom Watch founder Larry Klayman in a written statement.
The group filed a federal lawsuit in Florida, seeking to shut down the task force and block its proposals from implementation, the newspaper said.
The group maintains the task force violated the 1972 Federal Advisory Committee Act requiring presidential task forces to meet in public and publish notice of meetings in the Federal Register 15 days ahead of time.
The White House did not respond to a request for its reaction to the suit, The Hill said.
Obama outlined a package of gun-control legislation he wants Congress to pass and executive actions he intends to take in an attempt to ratchet down gun violence in the United States.