D.C. Council member Jim Graham is seeking to join the board of a government-controlled nonprofit group that funds youth organizations, touching off new concerns about the role of elected officials in directing the group’s activities.

The Children and Youth Investment Trust Corp. played a key role in a scheme by former council member Harry Thomas Jr. (D-Ward 5) to steal more than $350,000 in taxpayer funds by directing grants through the trust’s budget to favored charities that then gave him kickbacks. Revelations of Thomas’s scheme prompted investigations of the trust’s activities and debates over the group’s future.

Although no staff or board member at the trust was found to have knowingly participated in the scheme, the affair confirmed that council members were able to wield considerable influence over its activities.

Graham, who oversees the trust as chairman of the council’s Human Services Committee, had been one of the council members most active in directing grants through the trust. But after the Thomas affair, Graham (D-Ward 1) has used his post to aggressively investigate the nonprofit group’s dealings with Thomas and in other matters.

Graham said Friday that he asked Council Chairman Phil Mendelson (D) to appoint him to a nonvoting board seat earlier this year to make sure needed reforms are implemented.

“This is the current structure, and the current structure has people who are closely representing elected officials,” Graham said. “What the future issue ought to be is a separate issue.”

But the board’s chairman and a number of youth advocates are strongly objecting to the move, saying it sends the wrong message about the trust’s relationship with the city government and could harm efforts to secure additional private funding.

Board Chairman Robert C. Bobb, a city administrator under Mayor Anthony A. Williams (D), sent a letter to Graham on Friday asking him to withdraw his request.

Bobb wrote that he reacted to news of Graham’s request, published on The Washington Post’s Web site Thursday, with “great consternation.”

“I do not see what value would come from adding you as a nonvoting Board member,” he wrote.

“I believe that measures must be taken to prevent repeating the problems of the past by erecting a barrier between the Trust and elected officials. Appointing a Councilmember to the Board, even in a non-voting capacity, would not only represent a rejection of that idea but would essentially serve to institutionalize the very dynamic we are seeking to avoid.”

In an e-mail response, Graham suggested that the trust had dawdled in implementing recommendations of his committee and noted that the current oversight structure “anticipates political involvement in the Trust.”

A second exchange of letters took place this week, in which Graham and Bobb sparred over whether the trust had been sufficiently forthcoming in responding to Graham’s inquiries, including the status of an audit into the trust’s 2010 spending.

Mendelson said he had agreed to nominate Graham but indicated that the appointment would require a vote of the council’s 13 members. On Wednesday, Mayor Vincent C. Gray (D) called Mendelson to register his concerns about the move.

“The mayor shares some of the concerns that Mr. Bobb shared,” said Gray spokesman Pedro Ribeiro.

The vote could be uncomfortable for Graham’s colleagues. Groups that receive funding from the trust have lobbied against his appointment, said Maggie Riden, executive director of the Alliance of Youth Advocates.

“There needs to be a greater division between political influence and the operations of the trust if they are going to operate as they’re intended,” Riden said Friday. Graham’s appointment to the board, she said, would create “a clear and immediate conflict of interest.”

The trust’s board is composed of council and mayoral appointees. Three mayoral aides occupy nonvoting seats — Deputy Mayor for Health and Human Services Beatriz “B.B.” Otero, parks director Jesus Aguirre and juvenile justice director Neil Stanley.

But it would be unprecedented for an elected official to direct the trust, established in 1999 to marshal public and private funding to support and develop youth-oriented nonprofit organizations. In recent years, the trust has received the vast majority of its funding from the D.C. government.

Bobb said in an interview Tuesday that he would not object if a Graham staff member were to serve on the board. “I just have a fundamental disagreement with his appointment,” he said. “Send a staff person, but it doesn’t have to be him. I don’t understand what there is to be gained.”