The Fritz Pollard Alliance, which supports the promotion of minority coaches, front office and scouting personnel and is the main advisor to the NFL on race and recruitment, feels applying the rule to assistant and coordinator positions will pave the way for more minority head coaches.
"We believe that for the rule to be as effective as it can be it must be expanded to apply to offensive and defensive coordinators and assistant head coaches as well," the group said on Tuesday in a letter sent to several senior NFL officials.
"We believe pipeline issues are a part of the reason we've seen a reduction in head coaches of color over the past few years, and this expansion will diversify the head coaching pipeline."
The Rooney Rule was established in 2003 and requires NFL teams to interview at least one minority candidate for head coaching or senior football operation jobs.
NFL spokesman Greg Aiello told Reuters on Tuesday that the group's recommendations would be evaluated.
The rule was brought in to address the large gap between the amount of African-American players and number of non-white coaches and front office staff.
While the rule has been widely viewed as a success, leading to suggestions it could be applied to other sports leagues such as England's Premier League soccer championship, only four of the NFL's 32 teams have a minority head coach.
That total is the lowest amount since the Rooney Rule was implemented, a figure described over the weekend by the by the NFL as showing a "disappointing lack of diversity."
The group's suggestion comes shortly after the eight NFL head coaching vacancies at the end of the 2012 regular season were filled by white coaches.
The NFL's executive vice president of human resources, Robert Gulliver, said on the weekend that the lack of diversity needed to be addressed.
"The Rooney Rule has been a valuable tool in expanding diversity and inclusion in hiring practices but there is more work to do," Gulliver said in a statement.
"We have already started the process of developing a plan for additional steps that will better ensure more diversity and inclusion on a regular basis in our hiring results."
The NFL's four minority head coaches are Pittsburgh's Mike Tomlin, Minnesota's Leslie Frazier, Cincinnati's Marvin Lewis and Carolina's Ron Rivera.
The Super Bowl-bound Baltimore Ravens have an African-American offensive coordinator in former Indianapolis Colts head coach Jim Caldwell.