When news broke last week that the billionaire investor Joe Ricketts had considered financing a $10 million advertising effort linking President Obama with the fiery race-based rhetoric of his former spiritual adviser, the Rev. Jeremiah A. Wright Jr., Mr. Ricketts quickly distanced himself from the proposal and Mitt Romney’s campaign denounced it.

But Mr. Ricketts is continuing to play a provocative role in the effort to defeat Mr. Obama.

He is involved in another effort slated for this summer, a documentary film based on a widely criticized book, “The Roots of Obama’s Rage” by Dinesh D’Souza, which asserts that Mr. Obama is carrying out the “anticolonial” agenda of his Kenyan father.

Mr. Ricketts’s aides said he was one of roughly two dozen investors, providing only 5 percent of the film’s budget. But his involvement shows how the more strident attacks against Mr. Obama, which Mr. Romney’s aides view as counterproductive, continue to find backing even as the Republican Party and the Romney campaign seek to keep the focus on the economy.

The episode involving the proposed Wright advertisement put new attention on the ability of wealthy donors, working with groups independent of the candidates, to shape the presidential race, and stoked further debate about whether outside groups were driving politics to become increasingly negative.