The envelopes were intercepted at the sorting office in Mallusk
A bullet intercepted in the post on Wednesday was addressed to the home of Sinn Fein President Gerry Adams, the party has said.
Another bullet was actually delivered to the home of west Belfast councillor Paul Maskey, Sinn Fein MLA Conor Murphy said on Saturday.
A total of 12 envelopes, each containing a bullet, were addressed to Sinn Fein councillors.
Staff at the Royal Mail sorting office in Mallusk, outside Belfast, raised the alarm after finding the suspicious packages.
They were taken away by police for scientific examination.
Mr Murphy said that the act, in conjunction with the forklift truck attack on a bar in north Belfast on Friday by loyalist paramilitaries, the Red Hand Defenders, showed that a violent campaign was being intensified.
"Unionist politicians will no doubt continue to focus their attentions on the silent
guns of the IRA while ignoring and, in some cases, justifying ongoing unionist
paramilitary attacks on the nationalist community," Mr Murphy said.
"The hypocrisy of their
position is both breathtaking and indeed insulting."