SAN DIEGO — A judge said Friday he would issue a ruling next week in a lawsuit filed by Target Corp. against a San Diego pro-gay marriage group to make it stop canvassing outside the retailer’s California stores.

Minneapolis-based Target is seeking an injunction barring the activists from every outlet in the state, alleging they harass customers by cornering them near store entrances to discuss gay marriage, solicit donations and collect signatures on petitions for their cause.

Rights advocates say the legal battle between Target and Canvass For A Cause could further strain the retailer’s relations with the gay and lesbian community. Last year, Target made a $150,000 donation to a business group backing Minnesota Republican gubernatorial candidate Tom Emmer, who opposes gay marriage.

Target insists it remains committed to the lesbian, gay, bisexual and transgender community, and its lawsuit has nothing to do with the political agenda of Canvass For A Cause.

During a court hearing Friday in San Diego, Target attorney David McDowell told Judge Jeffrey Barton the case is about Target’s right to enforce its rules on its land.

“The question is Target’s property right and its right to exclude,” McDowell said.

Barton had asked McDowell why the company did not present testimony from customers complaining about the activists. McDowell said Target could get such testimony but he did not think that was necessary because it’s not the central issue.

Bryan Pease, an attorney for Canvass For A Cause, argued that sidewalks and areas outside stores such as Target have been considered by courts to be public domain for free speech. He said Target is taking action because it does not agree with the group’s message about gay marriage.

McDowell pointed out that the company has taken similar action against a number of organizations representing a variety of causes. Solicitors at stores have ranged from religious groups to charitable organizations.

“Whoever causes the most problems gets the attention,” McDowell said after the hearing when asked if all those groups have been subjected to legal action.

The corporation says at least eight Target stores in the San Diego area have received more than a dozen complaints daily since canvassers started working the locations in October 2010.

The activists have refused to leave when asked politely and shown the company’s policy prohibiting “expressive activity” on its property, Target said.

Canvass For A Cause director Tres Watson said Target wants to silence the 12,000-member group. “It’s very David vs. Goliath. … They’ve got all money in world to get us to stop talking about gay marriage.”

Volunteers are trained daily on being professional and polite, Watson said, and their aim is to educate the public about the rights of gays and lesbians.

Barton said he would issue a written ruling by the end of next week.

Target has said it was sorry for the hurt feelings caused by its contribution to the group supporting the Emmer campaign and tried to repair its image by creating a committee to help it better scrutinize decisions regarding financial donations.