SAG and the Alliance of Motion Picture and Television Producers met with a federal mediator last week in hopes of working out a new contract, as their most recent one expired June 30.
However, the mediator ended the session after little progress was made.
"We ask that you support your board and negotiating committee, and vote 'yes' to authorize the board to call a strike only if it becomes absolutely necessary," Rosenberg said in Wednesday's letter to SAG members. "Your leadership believes that we must be empowered with the real threat of a work stoppage in order to let management know that we are committed to protecting the future of all actors."
AMPTP issued a statement arguing the guild's latest mass e-mail "fails to justify why SAG members should bail out a failed negotiating strategy by striking during a time
of historic economic crisis.
"And it fails to explain why it makes sense to strike when SAG members will lose more during the first few days of the strike than they could ever expect to gain," AMPTP said.
Notable deaths of 2014 [PHOTOS]