By DARLENE SUPERVILLEWASHINGTON (AP) â¿¿ Responding to criticism from a fellow Democrat, the White House said Tuesday that anyone unhappy with the level of diversity in President Barack Obama's second-term Cabinet should hold the criticism until he completes it. White House spokesman Jay Carney commented in response to a letter to the president from Ohio Rep. Marcia Fudge, chair of the Congressional Black Caucus, in which she expressed concern that an African-American was not among the new members of Obama's Cabinet. "You have publicly expressed your commitment to retaining diversity within your Cabinet," Fudge wrote. "However, the people you have chosen to appoint in this new term have hardly been reflective of this country's diversity." Obama has named white men and women to oversee the departments of State, Treasury, Defense, Energy and Interior, as well as the CIA, the Environmental Protection Agency and the Office of Management and Budget. He was criticized for lack of diversity at the start of his second term in January after he named no women to several top posts. Carney said Tuesday that Obama is "deeply committed" to having a diverse Cabinet because he believes it makes for better decision-making. He encouraged critics to "assess the diversity of (Obama's) appointments once they've all been made." "There are obviously still appointments the president will be making," Carney said. "The president is committed to diversity. He believes that having a diverse Cabinet and a diverse set of advisers enhances the decision-making and deliberation process for him and for any president." Obama still must name new heads for the departments of Labor, Commerce and Transportation, as well as a new U.S. trade representative and head of the Small Business Administration. Labor was headed by a Latina, Hilda Solis, and Ron Kirk, the outgoing trade representative, is black. The president is close to naming Tom Perez, a Latino and Justice Department civil rights official, to succeed Solis, according to people familiar with the process who spoke on condition of anonymity because they did not have permission to speak for the record.