Minneapolis superintendent's supporters say the rule risks micromanagement and threatens her authority.
The board was expected to take up the policy on Tuesday but pulled it from the agenda, saying it and Johnson need more time for review.
Board member Richard Mammen proposed the compensation policy last month after Johnson decided in July, without board approval, to award $270,000 in retroactive raises to administrators.
Johnson later offered a mea culpa on the timing of the raises, which were awarded as the district cut more than 100 jobs, including 52 teaching positions.
Last week, members of the African American Leadership Forum, including former school board members Chris Stewart and Theatrice "T" Williams and City Council Member Don Samuels and his wife, Sondra Samuels, wrote to board chairwoman Jill Davis opposing the Employee Compensation Policy.
The letter expressed concern that the school board will use the policy to usurp the superintendent's authority.
"We understand the circumstances behind it, but this appears to be a permanent reaction to a temporary tension between the board and superintendent," the forum members wrote. "The proposed policy opens to door to unproductive micromanagement."
Stewart and Williams served on the school board with Davis when the panel hired Johnson as superintendent in early 2010.
"To aid her best work we prefer a board that supports the superintendent in public and disagrees with her in private," the letter said. "We believe this is particularly important during these times of intense scrutiny on the effectiveness of the school system."
A request from Johnson for more time to study the policy, not outside pressure, prompted board members to table their discussion, which could proceed during next week's school board meeting, school board vice chair Alberto Monserrate said.
The policy "was probably a little rushed," Monserrate said. "I just don't feel [the superintendent] had enough time to review it and make sure we got it right."
As justification for the bonuses, Johnson cited a $165,000 compensation study that found more than a third of senior management was paid below the average for people working similar jobs in other school districts.
The study indicated that women and minorities were being paid less than white men doing comparable work, said Bill English, a member of the African American Leadership Forum.
English and others pledged support for Johnson's decision in the letter, arguing that "there is no wrong time to do the right thing."
"It is troubling that the study revealed serious pay inequities in MPS, but we support the superintendent's decision to promptly address the problem," the forum's letter said. "Compensating staff equitably is the morally right, risk adverse, and legally astute thing to do."
The same compensation study found that 75 percent of Minneapolis employees are compensated above market.
Corey Mitchell • 612-673-4491