The Massachusetts Democratic Party today filed a federal complaint, charging there may have been illegal coordination between Senator Scott Brown’s reelection campaign and a group founded by Karl Rove that is blasting out robo-calls critical of Brown’s Democratic rival, Elizabeth Warren.

The state’s Republican Party then shot back, filing its own federal complaint charging similar coordination between Warren and AFL-CIO President Richard Trumka, who headlined a rally with Warren on Monday.

Federal election rules prohibit independent political groups such as Rove’s group, CrossRoads GPS, and the AFL-CIO, from coordinating directly with candidates.

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The Democrats’ complaint is part of an effort to draw attention to the involvement of Rove, George W. Bush’s former strategist, in the Massachusetts Senate race. In addition to filing the complaint with the Federal Election Commission, Democrats today dispatched Representative Michael E. Capuano of Somerville to hold a conference call with reporters blasting Rove’s efforts.

In their complaint, Democrats pointed out that Brown was seen by a Globe reporter speaking with Rove at a hotel restaurant during the Republican National Convention in Tampa. The Brown campaign has characterized the meeting between Rove and the senator as a chance encounter and said the robocalls were never discussed.

“The likeliest inference given this evidence is that Mr. Rove and Mr. Brown had a substantial discussion about the communications at issue in this race during this meeting,” the Democratic complaint stated. “It is also possible that Mr. Brown specifically requested or assented to the robocalls in Massachusetts for which CrossRoads GPS is responsible.”

Brown’s campaign declined to comment on the Democrats’ complaint.

But in its own complaint, the Republican Party’s accused the Warren campaign of illegal coordination with the AFL-CIO to “launch a direct mail campaign attacking Senator Scott Brown.”

“At a minimum, the AFL-CIO’s announcement of its endorsement and planned activities to support her candidacy constitute a suggestion and Ms. Warren’s presence at AFL-CIO events and continued close intereaction with the AFL-CIO constitute her assent,” the party wrote.

Eddie Vale, an AFL-CIO spokesman, said Trumka could not have coordinated the direct mail campaign with Warren’s campaign because it was finished five days before his rally with Warren in Boston.

“Clearly, there was no collusion between them,” Vale said.

The state Democratic Party did not immediately respond to a request for comment.

Both Brown and Warren have signed a pledge designed to prevent third-party groups from running television, radio and Internet ads in their race. The so-called People’s Pledge, however, does not prohibit those groups from contacting voters on the phone or through the mail. Unions that back Warren, for example, have been sending out mailers that attack Brown.