The decision emerged yesterday when the board unveiled the newly named Fundraising Promise, which supersedes the draft Donors' Charter.
It will form the basis of the new self-regulation scheme for fundraising, due to be launched to the public in the new year.
David Pitchford, founder of donor information website Intelligentgiving.com, said the decision gave charities a mandate to use manipulative tactics.
"Donors who are paying attention will be more alarmed than comforted," he said.
A source close to the board told Third Sector that some charities had objected to the rule during the consultation process this summer because they felt it was too subjective.
However, a board spokeswoman said the pledge had been removed as part of a move to consolidate the document. "Some promises were saying similar things," she said. "Principles have been reworked where there was an overlap, and that principle is now covered by promises to be respectful and to be fair and reasonable."
The new document features six promises to donors: charities signing up must commit to high standards, be honest and open, be clear, be respectful, be fair and reasonable and be accountable. "A robust fundraising promise will ensure accountability and greater confidence among the giving public," said Jon Scourse, chief executive of the board.
The board also unveiled research by Which? and YouGov that found that almost six out of 10 people (58 per cent) would be more likely to donate to a charity that was a member of the self-regulatory scheme.
Third Sector minister Ed Miliband urged charities to sign up. "The research clearly shows that self-regulation will boost public confidence," he said.