The sides have said they were divided over residual payments for DVD sales and terms covering other Internet content.
Three-year contracts with SAG and AFTRA covering theatrical movies and prime-time TV shows expire June 30.
AFTRA said it will impose a press blackout on details of its negotiations, which cover actors on prime-time TV shows such as "Curb Your Enthusiasm."
AFTRA announced last week that its members ratified a separate deal with producers on shows such as "Oprah" and "American Idol" with a 93 percent approval vote.
In a letter Wednesday to AFTRA members, union President Roberta Reardon cautioned that the federation expected "challenging negotiations" in the talks on the remainder of its TV shows.
AFTRA decided in March to negotiate with studios separately from SAG for the first time in about 30 years. It postponed its talks twice to allow SAG more time to reach a deal.
AFTRA said SAG made another request for more time and to negotiate together Wednesday, but declined.
"We believe it is in the best interests of our members, and our legal obligation, to proceed with our independent negotiations," it said in a statement.
Both actors unions and the alliance have said they want to avoid a rerun of the 100-day Writers Guild of America strike that shut down scripted TV production before it ended in February and cost the Los Angeles-area economy an estimated $2.5 billion.
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