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WASHINGTON – Two leading campaign finance watchdog groups called on the Justice Department Wednesday to appoint a special outside counsel to investigate what they called the “charade” of Jeb Bush’s non-candidacy for president.

Mr. Bush, the Republican former governor of Florida, has not yet officially announced that he is running for president, even as he has made speeches and appeared at scores of political events in New Hampshire, Iowa, Washington, California and elsewhere, raising millions of dollars through an outside “super PAC” that was set up to support his all-but-certain campaign.

In a letter to the Justice Department, the groups – Democracy 21 and the Campaign Legal Center – accused Mr. Bush of a monthslong “scheme” to evade campaign finance limits and other restrictions by not declaring himself a candidate.

The complaint charges that under the law, “Jeb Bush is a candidate for president,” whether he has officially acknowledged it or not.

The same two groups filed a similar complaint with the Federal Election Commission two months ago against Mr. Bush and three other would-be presidential contenders – Gov. Scott Walker of Wisconsin and former Senator Rick Santorum of Pennsylvania, both Republicans; and former Gov. Martin O’Malley of Maryland, a Democrat — over charges that all four were skirting campaign finance law by raising money without declaring themselves possible candidates.

But Wednesday’s complaint went further by taking the matter to the Justice Department to seek a criminal inquiry – an acknowledgment, the groups said, that “a dysfunctional and paralyzed F.E.C.” was unlikely to take action on the earlier request.

The letter to the Justice Department singled out only Mr. Bush because of what Fred Wertheimer, president of Democracy 21, said was his particularly “brazen and blatant effort” to evade campaign limits.

Kristy Campbell, a spokesman for Mr. Bush, dismissed the groups’ charges.

“We are fully complying with the law in all activities Governor Bush is engaging in on the political front, and will continue to do so,” Ms. Campbell said.

Asked to explain why Mr. Bush should not be considered a candidate after months of campaigning, Ms. Campbell said in an email to The Times: “Governor Bush is actively exploring a run. He has not made a final decision.There is nothing improper or unique about that. If Governor Bush engages in any ‘testing the waters’ activities, they will be paid for appropriately under the law and reported at the required time.”

The Justice Department said it would review the complaint but declined further comment.