The Republicans say they will voice their vote of no confidence at Wednesday's council business meeting and plan to ask Council President Teri Rennia to step down.
City Council Minority Leader Joe Mihalko and fellow Republicans Chris Papastrat and John Matzo also say they want the email's writer, Marty Doorey, to resign his post as chair of the Community Development Advisory Committee, which helps advise council on how to spend certain federal funds.
Lastly, they are asking the Broome County Board of Ethics to look into the matter.
The email in question was sent out by Doorey who was helping advertise for the coming vacancy of the deputy clerk position.
In the email, the deputy clerk's job description is given, which included the wording that the deputy is expected to participate in political activities and gather intelligence on council members and the mayor and report back to the majority on city council, which appoints the deputy clerk.
Minority Leader Joe Mihalko said the email is inappropriate and threatens the integrity of the legislative body.
He also said the press conference held by Democratic Councilman Bill Berg on Monday didn't adequately address the situation.
"We've lost some trust there. There was stuff going on, this whole thing of spying and I think it's just working against the mayor, working against the employees of the city and working against the Republicans on City Council. We're there, voted in by the residents, to do a job, to maintain things for the city and for the taxpayers," said Mihalko.
Democratic City Councilman Bill Berg said earlier this week that Rennia will not resign from her post, and that the deputy clerk would never be asked by council to spy on members or the mayor.
Berg said that Doorey had not done his homework before sending the message and that some of the wording was not appropriate, but he did not expect Doorey to resign.
Berg couldn't be reached for comment today.
Copyright 2016 Nexstar Broadcasting, Inc. All rights reserved. This material may not be published, broadcast, rewritten, or redistributed.