The Screen Actors Guild has told its members to back the WGA if writers go on strike — but only on the picket line.

In an email this week to its 120,000 members, SAG said its support of the Writers Guild of America is “steadfast.” It also urged thesps to walk WGA picket lines in their free time.

But SAG reminded its members that they still must work on projects if they’re contractually obligated to do so. SAG can’t strike until its contract expires June 30 as its current deal includes language that explicitly bars members from striking.

“If you are contracted to work on a show that continues to produce episodes, you are obligated by your personal service agreement and the ‘No Strike’ clause in our collective bargaining agreements to go to work,” SAG said. “You can continue to audition for work.”

The WGA returns to the bargaining table today with only six days left before its contract with studios and nets expires. Negotiating session with the Alliance of Motion Picture & Television Producers will be the first since Monday.

Reps for the Directors Guild of America and the American Federation of Television & Radio Artists said Wednesday those unions are also planning to provide their respective memberships with guidance about what they can and can’t do if the WGA strikes. Neither indicated when those missives will go out.

SAG and the Alliance of Motion Picture & Television Producers have not yet set a date for launching contract negotiations on that guild’s film-TV contract, but it’s widely expected that the Directors Guild of America will go first, possibly as early as next month. The DGA also faces a June 30 expiration but formed its negotiating committee early this year, while SAG has yet to take that step.

SAG negotiates the film-TV pact jointly with AFTRA.

SAG’s announcement of support for the WGA is a culmination of two years of efforts by both unions to seek a closer relationship following the 2005 election victories by SAG president Alan Rosenberg and WGA West prexy Patric Verrone, both of whom promised to take a tougher stand at negotiations.

SAG and the WGA jointly pressured companies last year for a “code of conduct” addressing how the industry deals with actors and writers in product-placement deals. And in recent months, SAG execs and leaders have attended the negotiating sessions between the WGA and AMPTP as observers.

In addition, SAG topper Doug Allen’s been particularly supportive of key WGA positions, such as opposing the AMPTP’s proposals for a three-year compensation study and a revolutionary revamp of residuals — taken off the table last week — that would pay talent only after basic costs have been recouped.

SAG said it sent out the message in response to the 90% support by WGA members for a strike authorization in results announced last week. It also indicated in its statement that it’s hoping the WGA won’t strike, although one is anticipated by many in Hollywood due to the lack of progress at the bargaining table.

“We continue to be hopeful that an amicable and equitable conclusion to their negotiations will occur,” SAG said in a statement.