"We do not believe in all good conscience that now is the time to be putting people out of work," it said.
Other signatories included Tom Hanks, Josh Brolin, George Clooney, Cameron Diaz, Heather Graham and Edward Norton.
The letter, sent to guild board members and staff, is the latest sign of unhappiness with the leadership of the 120,000-strong union.
On Friday, the New York representatives on the guild's board demanded a halt to the strike vote and called for an emergency meeting to replace the negotiating committee.
Guild President Alan Rosenberg planned an emergency meeting for Friday in Los Angeles, but rescinded it after New York members complained about the short notice to travel. A new meeting has not been scheduled.
The guild wants terms that are better than the deals accepted by directors, writers, stagehands and another actors union earlier in the year.
It is seeking union coverage for all Internet-only productions regardless of budget, residual payments for Internet productions replayed in ad-supported platforms online, and continued actor benefits during work stoppages, including those caused by strikes by other unions.
The studios have said it is unreasonable for the guild to demand better terms, especially now that the economy has worsened.
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