The five have grilled, among others, Mrs. Clinton; Barack Obama, when he was a 2008 Democratic presidential candidate; Gov. Terry McAuliffe of Virginia; and former Senator Christopher J. Dodd of Connecticut, who is now the chief of the Motion Picture Association of America. Senator Rand Paul, Republican of Kentucky, who is likely to run for president, has expressed interest in meeting with the women, as has Senator Elizabeth Warren, Democrat of Massachusetts.

“If you’re smart and you want to get ahead in politics, then if they ask you to dinner, you better go,” said Howard Dean, a former presidential candidate, a former chairman of the Democratic National Committee and a Colored Girls dinner guest.

The group, which does not include Ms. Rice, is composed of Ms. Moore, a top adviser in the Clinton White House who now works for the Dewey Square Group, a Boston-based consulting firm with an office in Washington; Ms. Brazile, who ran Al Gore’s 2000 presidential campaign and is now a commentator for CNN; the Rev. Leah D. Daughtry, a political operative who was the chief executive of the 2008 Democratic National Convention in Denver and was on the site selection committee for the 2016 convention; Yolanda H. Caraway, who got her start in politics by knocking on doors for Robert F. Kennedy’s 1964 Senate campaign and now owns a firm that does consulting work for Google; and Tina Flournoy, who was general counsel at the Democratic National Committee and now lives in New York and serves as Mr. Clinton’s chief of staff.

At times, Ms. Caraway has cooked for the political dinners and hosted the guests at her home, and on other occasions the women have reserved a back room at restaurants like the Hamilton or Ruth’s Chris Steak House, where they have typically remained until closing. “We never had an early dinner,” Ms. Brazile said. “People stayed and stayed.”