The mayor hopes that his idea will spread to other cities and organizations to create a wave of pressure on gun companies to follow his principles.
Nutter, president of the U.S. Conference of Mayors, has said that other mayors are looking into adopting measures based on Philadelphia's.
The original list included 20 principles, some of which were highly specific, such as how many serial numbers need to be printed on guns. The new version, however, has only six broader items, such as: "Make a commitment to develop, share and implement technology-enhanced safety measures for guns and ammunition."
City Solicitor Shelley Smith, who proposed the measure at the Pension Board, said that the changes were made at the suggestion of other cities that were considering following Philly's lead.
"In the mayor's discussion with other cities, there was a desire to broaden them rather than be so specific," she said.
The mayor and his spokesman later said that it was the administration that decided to boil down the principles to a shorter list.
Several of the companies that could be affected by the Pension Board's decision did not return requests for comment Thursday.
Jose Morales, who owns Philadelphia Firearms Training, a shooting range and gun-safety training center, said that Nutter's plan is a "strong-armed approach to be able to push his specific agenda through."
"If individuals would sit down honestly and all get together, every single face that this impacts, everybody come to the table, then these proposals would look a lot different," he said.
Morales, who has supported some gun-control efforts previously sought by Nutter, questioned whether the divestment threats will be effective.
"I have no issues amending some of my liberties if they can demonstrate to me that it's going to make a measurable impact on the level of violence," he said.
The city has previously adopted divestment resolutions with companies investing in Sudan, Iraq and Iran, as well as tobacco companies.
Also on Thursday, Nutter and Police Commissioner Charles Ramsey appeared in Washington, D.C., at a news conference announcing a bill introduced by U.S. Sen. Dianne Feinstein, D-Calif., that would ban assault weapons and high-capacity magazines, a policy Nutter has long called for.
On Twitter: @SeanWalshDN